I know that DES has a key length of 56, but what does the EDE mean and does it effect the key length?
In OpenSSL there is the des-ede-cbc option.
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Triple DES, DES-EDE or TDEA (formally speaking) can be used with no less than 3 key sizes.
The most logical form uses 3 separate keys for each of the phases (Encrypt, Decrypt and then Encrypt again, which is the meaning of EDE). It has a key size of 3 times 56 bits or 168 bits, but those are usually encoded with parity bits (the least significant bit of each byte), making 192 bits in total. Due to a meet-in-the-middle attack (already known at the design phase) the security is only around 112 bits, so don't be fooled by the key size alone. Generally we aim for 128 bit or higher security. This is sometimes DES-ABC - as in DES with distinct keys A, B and C.
The two key DES-EDE uses the same keys for the Encrypt phases. The key size is therefore 112 bits, encoded as 128 bits and a security of just around 80 bits, due to various attacks. For some attacks it might even be reduced to just over 63 bits. 80 bits is probably just a bit on the short side nowadays and it isn't recommended by NIST anymore. It is called the ABA key scheme, and technically you'd use BAB for decryption.
Finally single key DES-EDE is mainly used for backwards compatibility. The first encrypt and decrypt (or decrypt and second encrypt) cancel each other out so you're left with just one encrypt. You can guess the key size: 56 bits. Single DES can be easily brute forced, especially when hardware support is used. Single key TDES is never used in software and may not be supported (it just makes sense in hardware, where you don't want to supply a separate implementation of DES in addition to DES-EDE). I guess you'd call the key scheme AAA, but I haven't seen that name around at all.
DES-EDE is much slower than a good implementation of AES, and AES has a security of around 126,8 for a key size of 128 bits (using a very complicated attack). So if you have any chance, choose AES instead. AES has other advantages as well, such as the larger block size and lack of weak keys.
