I'll list some general things to check in the order I would isolate them.
- The bottom case itself is bent slightly compared to the frame (you should see wearing of the cases and brown dust where the parts rub)
- The plastic clips that hold your bottom case to the topcase are bent, not engaged, loose or damaged.
- A screw is not seated and rubbing. (and replace screw with cable, connector, lever, or cage - all of them are in there)
- Foreign debris came in from the exhaust vents and is stuck between parts where normal flex is causing a noise.
- Fan or blower bearings (unlikely - but I've seen/heard them make the darndest noises some times)
A great place to find pictures of your model is the iFixit repair guide - I'll use the Early 2011 15" iFixit guide for some tips below:
Look over your bottom case very carefully - you should see wear marks or fine dust or scratches where it is hitting the insides. If the noise is coming from the bottom case contact - you should see physical evidence of wear. If not, then focus on the other parts (fans, hidden debris stuck under the battery, board or other parts near the keyboard side of things, etc...)
It's probably from the bottom case, so look at all potential contact points where the bottom case can rub. When putting the bottom case on again, remember where these inserts are so you can press them and hear a click for each before screwing the fasteners. When open, inspect the clips very well - a broken clip or not getting the insert into the snap is a big cause of the bottom case moving around when in use.
Similarly, pay attention to the clearance between the battery indicator, keyboard ribbon ZIF socket and trackpad connector cage as well as the clips under the left hand side of the mac. Even a battery screw could be too high and scraping the case. Once you have exhausted the easy things, you may even need to remove and re-seat the components on the left hand side of the mac to ensure nothing is stuck under the topcase and between the components.
Unless you are a very good tech and know what things cost should they break, it might be better to take it in for service - especially if you can show the tech how to reproduce the noise. There are so many components, any one of which could be harboring a loose screw or piece of debris that made it's way in the heat exhaust vents - it's hard to guess what exactly is making your mac squeak.