Learn to use the diode test on your DMM.
Transistors, you can at least figure out if they ARE trasistors or FETS. And with a scope and a signal generator, you could at least quantify their performance; or with a project, you could find out if they are good enough or not. 3 pin parts can also be diodes. Or voltage regulators. Or voltage detectors. Or.. well, I dunno what else.
Anything with four pins, you should maybe at least test to see if it's an optocoupler or an SSR. Optocouplers because they're common. SSR's because they are unreasonably expensive, for some reason. So even if it's a long shot, at least take a crack to see if it's an SSR.
Anything with 5-6 pins might be an opamp or a comparator. But good luck with that, since there are several pinouts for those types of parts and testing requires more external components. And dozens of other things they could commonly be.
Eight pin IC's I'd at least check for possible FET. They have standard pinout, so easy to test, anyway.