It sounds like you've been pretty thorough checking what it could be. I've had clicking caused be a loose quick release, and that was difficult to figure out. A few things you might have missed...
Check the saddle rails, both where they clamp to the seatpost and where they go into the seat itself. Or try pedaling standing up.
Make sure the headset is not loose. Even without your hands on the bars there is still some lateral force there when you pedal.
Inspect the frame for cracks, paying attention to welds since they are high stress areas and likely to crack if not done correctly.
Put the bike on a stand, or turn it upside down, and pull the chain off the crankset. See how it feels when you turn the crankset by itself. If it feel rough it could be bad bearings. See if you can put force on it in a way that will make it creak. You might not be able to since it's hard to put a lot of force on it without the resistance of the chain.
The bottom bracket could just be loose. If it's a thread-in style, it's easy to tighten with the correct tool. I recommend using a torque wrench because the torque spec is high and you are likely to stop before you reach it if you are tightening by hand. See here for common torque specs:
http://www.parktool.com/blog/repair-help/torque-specifications-and-conceptsWhile you're at it, make sure the crank arm bolts are tight enough. Those need fairly high torque, too. The pedals don't need much torque, but you should use grease or anti-seize on the threads when installing.
It could also be a problem with the freehub or cassette. If one of those is loose it could make noise, or the bearings in the freehub could be worn out. Taking off the cassette, cleaning and greasing the splines, and putting it back on is easy. Taking off the freehub is more difficult if the hub is shimano style cup and cone since it involves disassembling the whole hub. On my fancy cartridge bearing wheel all I have to do is pull hard and the freehub pops off!
