Are transponder codes 7701 - 7777 ever used?
Yes these codes are used. Only 7700 is used to denote emergencies, and usually only if you aren't in contact with ATC, or can't get their attention(frequency is packed). Codes in this range are allocated according to the National Beacon Assignment Plan in the US. There are other codes that are assigned for various issues, 7777 as mentioned in the comments is assigned, and I've assigned others in that range before, same with the 7600 and 7500 ranges.

If you're already in contact with ATC, and they have you tagged, it is very easy to mark you as an emergency and have it light up on everyone in the facility's scope.