Sorry we got distracted by the debate.
Long story short with what exists right now you can going to have to encode your video into something else to watch it, we were just debating what could happen in theory.
The main problem is MKV is not all that good as storage to convert later on (most tend to use it as a final storage due to it accepting things others do not like variable frame rate).
I am not sure about the existing H264 support of the wii and if you will be able to get away with transcoding to a lower resolution.
Still option 1: if you are using SMB then you might be able to use your PC as a backend and encode on the fly into something else.
Simple way is something like:
http://tversity.com/download/features/
More complex than that (not tried this one yet):
http://forum.doom9.org/showthread.php?t=133313
If you are using a USB drive then you are going to have to encode it to something else beforehand. There are many encoding guides all over the internet for this one although I will point to MKVextract as part of the MKVtoolnix kit (there is a third party GUI from what I recall):
http://www.bunkus.org/videotools/mkvtoolnix/
As for how much if you are already going that route and only intend to use it for the wii downscale directly to 480 vertical height (I do not know what the horizontal res is here but keep aspect ratio, I know you said 720p but in my experience that can still mean anything) and go with higher bitrate or quant xvid.