The strings vary and the volts for the twinkle lights vary also. Normally I think 1.5-3V. I used to mess with them allot but it's been awhile. I think the superbrights are 3V. The other normal ones I think are 2V but work on 1.5V I think.
As far as amps, I don't know. Can't be much, I have ran them for fairly long periods on AA,C,D batteries in the past. I've ran them on 12V but right now can't remember how many I ran in series to do it.
I should have a bunch around here, but this time of year they will be burried agian somewhere already, I have limited space now and everything is burried under something.
I'll try to find some and test them within a few days, if you need some I might be able to send you a dozen or more free since now they may be hard to find in stores also.
E-mail me if you want, though I have not been online allot recently but I will answer when I am. If you want when I find them I can also try to test the temps with the Non-contact thermometer.
I should also start testing them for some of my own projects needing minor heating.
Being low volts like they are I can wire any number in series for almost any volts I want. When one burns out the rest stay lit (but burn at a higher volt ) so the entire string does not go off. The really old ones if one went out they all went out, but anything in the last few years (maybe 5-10) should not do that.
I was going to build a small Egg incubator soon and lots of these twinkle lights on some 19.2V battery packs may be just right 
Anyone wanting to play with these, watch the Thrift stores, they get allot of them often and sell then cheap normally. May want to ask for them if you don't see any, they may have some but mostly put them out around the holidays.