So I've had this issue with my road (entry level) bike for quite a while now, that has been driving me insane. It would happen whenever I pushed down on the pedals, putting my weight on them. Whether I was on or off the saddle didn't make a difference, and I couldn't pin point whether it was coming from the left or right. I was convinced that the problem was with the bottom bracket, which was, ironically, the only component that I dont have the tools for to disassemble.
Today I decided to try messing around with what I was convinced was NOT the problem--my pedals. So I unscrew them, brush off any particles of dirt, grease up the components and the threads (my first time greasing the threads), and tighten everything back up. So I put on some shoes, hop on, and what do you know? No clicking. I get back home, get dressed, and hurriedly jump on my bike to test it out before it got real dark. I climbed all of the steep hills, I forced all of my weight on my pedals, and the only sounds that came from my bike were the soft clicking of my cateye, and the rubber hugging the pavement.