Unless the ammo was bad to start with age shouldn't have any effect. I'm shooting x54R surplus from the 1970's without issue and millions of rounds of x39 and x54R from the 60's, 70's, and 80's are shot in Canada every year without any problems.
A crooked bullet wont give you ideal accuracy but so long as it chambers it shouldn't be dangerous. If it's crooked because something is stuck in the case between the bullet and neck that could be an issue.
7.62x51 NATO has a lower pressure than 308 Winchester but also uses a different location in the chamber to measure the pressure from. Pressure measured from different places in the chamber can yield different pressures with everything else being identical. It's a hotly debated topic all over the place (not just on the internet). Some say it's perfectly safe, others say it can damage your firearm, and some say it's downright dangerous.
Personally I shoot 7.62NATO ammo in 308 Winchester civilian rifles and have never had a problem. I also have shot 308 Win ammo in 7.62NATO firearms without any issues. That's just me though.
One issue that can happen regardless of which side you are on is the harder primer cups in NATO spec ammo can sometimes have issues being set off by weaker firing pin springs in civilian rifles. Savage and Browning seem to be the most common brands with this issue. It could work perfectly, it could take 2-3 strikes on the odd round to set if off, or the ammo might not work at all in a give rifle. My Rem 700 has no issues with 7.62NATO ammo but my Savage Axis does get the odd round that requires a second strike to set off with 5.56NATO ammo. I once got a box of free 7.62NATO ammo from a guy with a Browning. He said they where all duds and was throwing them out. I loaded them in a Norc M305 I had at the time and they worked fine.
The only lab tests I've read about comparing the two was for .223 Rem and 5.56NATO. The only dangerous pressures where encountered when shooting 62gr green tip US surplus 5.56NATO ammo in a minimum spec, match grade, .223 Rem chamber. It went to 72,000psi or something I believe so still within proof levels but not healthy for the rifle.