Looking through the terms and conditions for different affiliate networks, i haven't found much that says anything about you can't be on azoogle and also be on neverblue, or others, etc... is there anything anyone knows about not being allowed to run (on different sites) offers from different networks?
No you can be on all of them. One thing that are in some terms are that you can not disclose the amount you are being paid on your offers from one network to another. This is usually done to get raises in your offers you are running.