Or... some things you can do with the audio in AVI home movies :)
See also Audio Improvement guide

Programs/Filters
GoldWave (Get plug-ins)
Moonlight Odio Dekoda V1.23 DirectShow® filter
Download MoonLight Odio Dekoda v.1.23
HeadAC3he v0.23a (Get Dlls, see Readme.txt)
Fraunhofer MP3 professional > KaZaA :)

Vdub
file > file information
This should tell you what you have.

Included in this guide are the most often used methods of saving and converting the sound track, although quite a lot of people do this by default, to use it later with programs like TMPGEnc, this is not always necessary, and at times can lead to more problems like lip sync. However the guide is not about why you should do it, its about how you can do it.

Vdub
Lets start with the most often used method, Vdub. In this example the audio is MP3

Audio > Direct stream copy
SAVE WAV
This saves out the audio stream "As Is" what ever it happens to be, so the file you made may not be a WAV (It may be AC3). If you right click the .wav you saved it will tell you the format it is, in this example it says "MPEG Layer-3,56 kBit/s, 24,000 Hz, Stereo" A MP3 made at 56Kbit/s at 24,000Hz, file size 24K you need to rename it to .mp3 to be compatible with playback devices, although those devices would probable play them no matter the extension is called.

The next method used in Vdub is Full processing mode (No use for AC3)
Audio > Full Processing Mode
Audio > Conversion
Convert to 44.1Khz (ready for VCD) or leave it save as default.
In this example the original is 24Khz
Default compression is PCM
SAVE WAV

Right click the file you saved, and it will reveal it has been uncompressed and converted to 44.1Khz. In this example the file is very large and its details are "PCM,44,100 Hz, 16 Bit, Stereo" file size 623K

Those are the most often used methods, however a lot of people have been experiencing problems with some files that contain AC3
If your sound is AC3, you must use Direct Stream Copy

Audio > Direct stream copy
SAVE WAV
Now rename that .wav to .ac3 and follow on below with Headac.23a

Headac.23a
Again there are many programs that can be used to convert AC3 to WAV, in this guide I have only included one of the most popular.

Just click the source button and select your .AC3 file, then click the Destination button to select where to store the file. If there are other language streams present, you might also be able to select them. Click start to make the WAV file

Gold Wave
Gold wave can load the audio direct from AVI files, it can also load AC3 streams

Once loaded, you can save out the stream as a 16 bit stereo, Gold wave cannot handle the 6 channels, it will only use left and right channels of a AC3 stream, but these might be the ones you want anyway.

TMPGEnc
Yes you can even do it with this program.
Browse and select your AVI then select File > Output to file > WAV

Click the Setting button to select the compression you want, DivX PCM etc

Before you can work with these audio streams, you need to install supporting codec/filters. You wont be able to load a MP3 sound track if you don't have an MP3 codec. Luckily there are only a few audio codecs being used in AVI files. There has also been a problem where the MP3 codec you installed is a Trialwear or a freeware and may only support bitrates up to 128K and the AVI you have might have a bitrate much higher. Codec packs like Nimo don't provide the full version.

Update, Missing Audio
There have been a few home movie AVI's with missing audio at the end, reports are about 6 seconds, Those 6 seconds of "Blank" do not have a silent audio stream, so the audio is missing. Any attempt to save video and audio, would then give a big difference in length (In this case 6 seconds). If you see a big difference when loading the stream, then you will know you have the missing audio stream.
Vdub MP3
Go to the end of the AVI, and come back a few minutes then press play, press stop as soon as the audio is not heard, then click the keyframe back once and mark that as start. Then move to the end of the movie and mark that as end. Delete those frames and save out another copy using video/audio direct stream copy. You have now removed the frames that have no audio, and can reload that back to work on as normal.