CRC stands for cyclic redundancy check. It checks the integrity of the file to make sure there are no errors from the original source.
SFV stands for simple file verification. It's a simple way to verify files are identical to the original source. It's basically a file that has the following format
; comment, anything with a semicolon is a comment
; more comments
; created by <program name> on <date created> (usually automatic stuff the program puts in here
some file name.some extension <checksum>
; ie
01 some_mp3_title.mp3 0B034ACF
MD5, I forget what it stands for, but it's more advanced than SFV. SFV has some sort of flaw (mathematical, the way it calculates the checksum) insofar as it can't have unique values above a certain filesize limit. I forget the exact size, but if it's a large file, it has a chance of having the same checksum as a smaller file. MD5 uses larger checksums and a more advanced algorithm to calculate it.
There is a program, I Forget the name, but it embeds the CRC value of the mp3 into the id3 tag and verifies it with the audio stream to make sure you file is correct. This isn't standard, though. It also doesn't work on VBR files, since it can't read the audio stream right (if I Remember correctly), so it's basically useless for most of us that encode in vbr.
SFV is all you'll ever need for audio sharing, since mp3 files rarely exceed 15mb and it's a simple way of verifiying that there were no problems during download. MD5 is mostly for verification on very very large things, I think. Like hard drive images, large programs, stuff like that. The chances of you having the same CRC for two different mp3s is highly unlikely.
Hope that answers any questions. :/