I believe some (all?) implementations of DES use only 7 bits per character of the key (ASCII encoding). I'm not sure if the definition of DES allows for 8-bit characters in keys or if it actually ignores the high bit of each byte. I think it's the latter.
However, in .NET key sizes are based on the number of bytes, times 8 bits per byte, even if the underlying algorithm ignores that top bit. That is probably the main discrepancy.
TripleDES runs DES three times with potentially three different 56-bit DES keys. In some implementations the middle run is reversed (encrypting-decrypting-encrypting or "EDE") so that using the same 56-bit DES key for all three duplicates the encryption of simple DES. This was done for compatibility with older systems where both are using hardware-based encryption. I'm not sure if the TripleDESCryptoServiceProvider uses this "EDE" approach or the "EEE" approach (or gives you a choice). Further, the same 56-bit DES key can be used for the first and third run, using a 112-bit key instead of the 168-bit key it could also use.
The certified TripleDESCryptoServiceProvider wouldn't accept 56-bit (64-bit) keys because it's not really 3DES security (you could use DESCryptoServiceProvider instead?). At one time it was determined that the 168-bit EEE (or EDE?) 3DES does not provide any greater security than using a 112-bit (128-bit) key. However, there may be some extreme (generally unavailable) attacks in which the shorter key is theoretically more vulnerable. That may also apply to the EDE vs EEE question.
On your compatibility vs other languages question, .NET's *CryptoServiceProvider classes are just a wrapper API around the underlying Windows CRYPTO library. If the other languages are also using the Windows CRYPTO library it should be compatible. Otherwise, you'd have to find out whether they are using EDE or EEE and make sure all are using the same one (you may or may not have flexibility on that), and obviously use the same key length. They are probably all using the same byte order, but if you find things still don't match up that might be another thing to check. Most likely on Windows they're all using CRYPTO and will probably match up as long as you can set the options the same way for all of them.