That is a 2.4L 4 cyl. The 22 is model #, not displacement. The 20R is a 2.2L, but was upgraded to the 2.4 in '81.
I agree with the valve adjustment - usually goes a long way, but my recommendation - and I work on a lot of these, specializing in RWD Celicas- is adjust them HOT, and one cyl at a time - #1 TDC, timing mark aligned, adjust intake and exhaust, turn engine 180 degrees, adj #3, then another 180 degrees and the timing mark will line up again for #4... Oh, and adjust to a "modified" .007 intake and .010 exhaust.
If you are looking to replace the engine, use an '85 and later engine, as they have a slight bit more power due to a complete redesign by Toyota, and ensure that it is rebuilt with a steel timing chain guide!