Multimeters are very good tools to find out problems in electronics circuits and testing electronics components. Resistor measurement is found in practically all multimeters, capacitance measurement range is becoming more and more common and some high-end models can also measure inductance. Many multimeters have also possiblity to test bipolar transistors (Hfe measurement range), but I don’t remeber that I would have seen any multimeter that has measuring range for FET testing. Properly testing all properties of a MOSFET requires a lot of expensive test gear. What would be useful is a way to easily have a working or not working result with some simple test that can be made with a normal multimeter and maybe few other components.
MOSFET TESTING page published by Integrated Publishing gives you idea how to test P-channel FET, N-channel FET and MOSFET with a multimeter. Testing a MOSFET web page gives you a simple testing procedure is for use with a digital multimeter. For the provedure to work you need a digital multimeter in the diode test-range with a minimum of 3.3 volt over d.u.t. (diode-under-test). If your multi-meter is less than that it will not do the test. 4QD Tec MOSFET testing page starts by giving a pretty similar test procedure, but continues with an improved test setup that need few extra components.
Please note that MOSFETs are very sensitive to electrostatic charges and can be easily damaged by them. A vacuum plunger (solder sucker) must not be used because of the high electrostatic charges it can generate. Solder removal by wicking or using professional ESD safe tools is recommended. It is also good practice to wrap MOSFETs in metal foil when they are out of a circuit.