I'm thinking that your neck may be bent, even a minor warp in the wood could mess it up.
That or you have the strings "over tuned". This means the say you tuneing E but you turn it to far what happens is that the tuner reads it as normal and you can hear it normal but when you play diffrent frets its out of tune.
I don't have a tremolo. I'm using .10's. They're fine for a Paul.
If you're insinuating that I have a bad guitar choice, loving leave. I need help.