The wineasio DLL must be registered in the wineprefix.
For both 32 and 64 bit wine do:

# regsvr32 wineasio.dll

On a 64 bit system with wine supporting both 32 and 64 applications, regsrv32
will register the 32 bit driver in a 64 bit prefix, use the following command
to register the 64 bit driver in a 64 bit wineprefix:

# wine64 regsvr32 wineaiso.dll

Note: regsvr32 registers the ASIO COM object in the default prefix "~/.wine".
To use another prefix specify it explicitly, like:

# env WINEPREFIX=~/asioapp regsvr32 wineasio.dll