I'd still like to know what is in the .mkv file. The codecs used may be fine in an avi container...may not...can't tell without more information.
In any case, if you want to encode to a different configuration see if you can follow these instructions. After you open AviDemux and import your video, you should look at the three main controls next to the video window. The top one is Video. Change it from Copy to Mpeg4 ASP (Xvid). It is the very last entry on the drop down list. Click on Configure if you want to change the encoding parameters, like making it do a two pass encode for higher quality.
Next, look at Audio. I'm not sure what you are starting with, or the best codec for you to use, since you stated purpose is to use clips in dvds. Normally I'd say use AC3.
The last one is Format. It should be set to AVI.
Make sure to put an .avi extension on your output file name.
Now, having said all that, you can also use AviDemux to convert to mpeg2, which is the codec used in dvd-video. I prefer other tools for that, but can be done here. Use DVD in Video, AC3 in Audio and Mpeg TS (A + V) in Format. Be certain to put an .mpg extension on your output file when doing this.