This is somewhat but not really working.
The WM_IME_COMPOSITION message carries the last IME character modified. By evaluating lParam it is possible to filter when there's actually something to be done, as this message fires more or less all the time you fiddle around with IME thingy.

Problems:
I think the result is DBCS and not real Unicode
Only one character can be caught this way. All others are still a nasty "?"

A message logger is included (some spam stuff like mouse move events excluded).
I also tried fiddling with PeekMessageW as it was done in some Visual Basic stuff, but this does not seem to help here, although the "?" problem seemed similar.

There is no visual output. Play around and check messages.txt afterwards.

Code:
#include <acknex.h>
#include <windows.h>

#define WM_INPUT 0x0099
#define WM_UNICHAR 0x0109
#define WM_IME_CHAR 0x0286 

long WINAPI PeekMessageW(long lpMsg,long hWnd,long wMsgFilterMin,long wMsgFilterMax,long wRemoveMsg);
#define PRAGMA_API PeekMessageW;user32!PeekMessageW

WPARAM unichar = 0;
WPARAM resultchar = 0;
MSG msg; 
var file;
STRING* msgstr = "#300";

LRESULT CALLBACK OriginalHandler(HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam);

LRESULT CALLBACK MyMessageHandler(HWND hwnd, UINT message, WPARAM wParam, LPARAM lParam)
{
	if(message >= WM_INPUT && message != WM_MOUSEMOVE && message != WM_ENTERIDLE && message != WM_NCMOUSEMOVE)
	{
		str_printf(msgstr, "message : <0x%x>, WPARAM : <%d>, LPARAM <0x%x>.rn", message, wParam, lParam);
		file_str_write(file, msgstr);
	}

	if (WM_IME_COMPOSITION == message)
	{
		unichar = 0;
   	//if (PeekMessageW(&msg, hwnd, WM_IME_CHAR, WM_IME_CHAR, PM_NOREMOVE))
   	
   	if (lParam == (GCS_RESULTREADSTR|GCS_RESULTREADCLAUSE|GCS_RESULTSTR|GCS_RESULTCLAUSE))
   	{
				//next message will be char transfer, so grab char of last ime change
   			unichar = wParam;
   			str_printf (msgstr, "IME CHAR cached: %d.rn", unichar);	
				file_str_write(file, msgstr);
		}
	}
	
   if (WM_CHAR == message)
   {
			str_printf (msgstr, "WM_CHAR received - real: %d cached: %d.rn", wParam, unichar);	
			file_str_write(file, msgstr);
	   	if (unichar != 0) 
	   	{
	   		resultchar = unichar; 
	   		unichar = 0;
			}
			else
			{
				resultchar = wParam;
			}
		//now do something useful with resultchar
   }
   return OriginalHandler(hwnd,message,wParam,lParam);   	  
}

function main() 
{
	file = file_open_write("messages.txt");
   OriginalHandler = on_message;	// store the original message loop
   on_message = MyMessageHandler; // and replace it by your own
}



Sample message log:
Code:
message : <0x210>, WPARAM : <262146>, LPARAM <0x14105c>.
message : <0x31f>, WPARAM : <1>, LPARAM <0x0>.
message : <0x100>, WPARAM : <81>, LPARAM <0x100001>.
message : <0x102>, WPARAM : <113>, LPARAM <0x100001>.
WM_CHAR received - real: 113 cached: 0.
message : <0x100>, WPARAM : <87>, LPARAM <0x110001>.
message : <0x102>, WPARAM : <119>, LPARAM <0x110001>.
WM_CHAR received - real: 119 cached: 0.
message : <0x101>, WPARAM : <81>, LPARAM <0xc0100001>.
message : <0x101>, WPARAM : <87>, LPARAM <0xc0110001>.
message : <0x100>, WPARAM : <69>, LPARAM <0x120001>.
message : <0x102>, WPARAM : <101>, LPARAM <0x120001>.
WM_CHAR received - real: 101 cached: 0.
message : <0x101>, WPARAM : <69>, LPARAM <0xc0120001>.
message : <0x2a2>, WPARAM : <0>, LPARAM <0x0>.
message : <0x11f>, WPARAM : <-2139094504>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2013069312>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2138046448>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2138046449>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2138046450>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2013069312>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2139094924>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2139094916>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2138046454>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2138046455>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2139094918>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2139094920>, LPARAM <0xd8350887>.
message : <0x11f>, WPARAM : <-2139094922>, LPARAM <0xd8350887>.
message : <0x215>, WPARAM : <0>, LPARAM <0x0>.
message : <0x11f>, WPARAM : <-65536>, LPARAM <0x0>.
message : <0x2a2>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <8>, LPARAM <0x0>.
message : <0x10d>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <269>, LPARAM <0x0>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19ee08>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19ee08>.
message : <0x282>, WPARAM : <5>, LPARAM <0x1>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19f888>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19f888>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0x282>, WPARAM : <4>, LPARAM <0x1>.
message : <0x100>, WPARAM : <229>, LPARAM <0x1c0001>.
message : <0x10f>, WPARAM : <113>, LPARAM <0x1e00>.
IME CHAR cached: 113.
message : <0x286>, WPARAM : <113>, LPARAM <0x1>.
message : <0x286>, WPARAM : <119>, LPARAM <0x1>.
message : <0x286>, WPARAM : <101>, LPARAM <0x1>.
message : <0x10e>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <270>, LPARAM <0x0>.
message : <0x102>, WPARAM : <113>, LPARAM <0x1>.
WM_CHAR received - real: 113 cached: 113.
message : <0x102>, WPARAM : <119>, LPARAM <0x1>.
WM_CHAR received - real: 119 cached: 0.
message : <0x102>, WPARAM : <101>, LPARAM <0x1>.
WM_CHAR received - real: 101 cached: 0.
message : <0x101>, WPARAM : <13>, LPARAM <0xc01c0001>.
message : <0x10d>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <269>, LPARAM <0x0>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19ee08>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19ee08>.
message : <0x282>, WPARAM : <5>, LPARAM <0x1>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19f888>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19f888>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0x282>, WPARAM : <4>, LPARAM <0x1>.
message : <0x100>, WPARAM : <229>, LPARAM <0x1c0001>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1e00>.
IME CHAR cached: 51842.
message : <0x286>, WPARAM : <63>, LPARAM <0x1>.
message : <0x10e>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <270>, LPARAM <0x0>.
message : <0x102>, WPARAM : <63>, LPARAM <0x1>.
WM_CHAR received - real: 63 cached: 51842.
message : <0x101>, WPARAM : <13>, LPARAM <0xc01c0001>.
message : <0x10d>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <269>, LPARAM <0x0>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19ee08>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19ee08>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <5>, LPARAM <0x1>.
message : <0xc055>, WPARAM : <1>, LPARAM <0x19f888>.
message : <0x288>, WPARAM : <6>, LPARAM <0x19f888>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1b9>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0xb0>, WPARAM : <1701960>, LPARAM <0x19f84c>.
message : <0x282>, WPARAM : <4>, LPARAM <0x1>.
message : <0x100>, WPARAM : <229>, LPARAM <0x1c0001>.
message : <0x10f>, WPARAM : <51842>, LPARAM <0x1e00>.
IME CHAR cached: 51842.
message : <0x286>, WPARAM : <63>, LPARAM <0x1>.
message : <0x286>, WPARAM : <63>, LPARAM <0x1>.
message : <0x10e>, WPARAM : <0>, LPARAM <0x0>.
message : <0x282>, WPARAM : <15>, LPARAM <0xa790bff>.
message : <0x282>, WPARAM : <270>, LPARAM <0x0>.
message : <0x102>, WPARAM : <63>, LPARAM <0x1>.
WM_CHAR received - real: 63 cached: 51842.
message : <0x102>, WPARAM : <63>, LPARAM <0x1>.
WM_CHAR received - real: 63 cached: 0.
message : <0x101>, WPARAM : <13>, LPARAM <0xc01c0001>.
message : <0x2a2>, WPARAM : <0>, LPARAM <0x0>.
message : <0x281>, WPARAM : <0>, LPARAM <0xc000000f>.
message : <0x281>, WPARAM : <1>, LPARAM <0xc000000f>.
message : <0x2a2>, WPARAM : <0>, LPARAM <0x0>.
message : <0xa1>, WPARAM : <20>, LPARAM <0x1610524>.
message : <0x215>, WPARAM : <0>, LPARAM <0x0>.
message : <0x112>, WPARAM : <61536>, LPARAM <0x1610524>.
message : <0x2a2>, WPARAM : <0>, LPARAM <0x0>.
message : <0x281>, WPARAM : <0>, LPARAM <0xc000000f>.
message : <0x102>, WPARAM : <32>, LPARAM <0x0>.
WM_CHAR received - real: 32 cached: 0.



character list, which does not seem to match to what I clicked on IME keyboard:
http://thinkingstiff.com/characters.html