MKV is a container just like AVI.
You should (assuming the streams are compatible with AVI) be able to remux it with "avi mux gui"
http://www.alexander-noe.com/video/amg/
That certainly beats transcoding.
HOWEVER
Since you're using a DVD player to play these on, chances are it only supports MPEG-4 part 2 (Xvid or DivX rips) rather than MPEG-4 part 10/H264/AVC (x264 rips) which is the standard with anime fansubs (the anime fansub scene tends to opt for Xvid+AVI or x264+mkv rather than any other combination) and therefore your best bet for watching it on your MPEG-4 part 2 enabled DVD player is for you to transcode it to Xvid+AVI.
Use a tool such as "media info" to find out what video format a video is
http://mediainfo.sourceforge.net/en
I find the easiest transcoding tool is mediacoder. You'll want to transcode it to Xvid at 2-pass, mp3 or AVC audio and output to AVI.
http://mediacoder.sourceforge.net/
(Re)muxing: Putting video/audio/meta-streams into a file container format without modifying the streams
Transcoding: Converting video/audio from one standard to another using a codec
MPEG-4 Part 2: Most non-high def video floating around these days is encoded in this format. It is typically Xvid or DivX (DivX players are included in most modern DVD players)
MPEG-4 part 10: also known as H264, this standard is the current highest video quality format that exists. It typically uses more power to decode than other, lower quality video.