Without precision instrument, what specs can I use to check if it is not LM358 or TL082 inside? I used to check my OP07C by GBWP, by attempting to run 1MHz through it at gain 2, which will success on both TL084 and LM358 but fail in OP07C.
There are parameters that are a dead giveaway if the "replacement part" is extra crappy - input current, offset voltages and such, but if they are in the same general area, well, that's a problem.
One way could be to compare it against a known real one - measure each parameter (supply current included ) for many situations and if the parameters are off enough, then you probably have a fake part. However this is not 100% obviously. And you do need SOME precision instruments.
But if in doubt, DON'T use the part - even if the parameters check out it could be a factory reject, something prone to failure, something very similar.