Testing crystal oscillator with multimeter crashes system
Most of the time the pc crashes as soon as I touch 1 of the 2 leads. [...] Is this normal and as such not the proper way to test ?


Yes, that's expected behaviour. As already mentioned in comments, the actual crystal drive is very low power and so it's sensitive to any additional loading.

Your multimeter is likely designed to measure the frequency of (relatively) low impedance e.g. logic level signals. Even so, its additional loading might still cause problems, depending on the multimeter.


  Is there another way to determine the crystal is in good working order ?


On an IBM PC or PC/XT, the crystal is connected to an Intel 8284A clock generator IC, to perform the necessary division of the crystal frequency for the CPU and other clocks, and generate the appropriate logic level signals.

There are a number of tests you could do. I'd start with measuring the OSC output (pin 12 of the 8284A) which is a logic-level buffered version of the crystal frequency, so you should measure 14.31818 MHz there. (Be careful of possibly shorting other pins on that IC when making measurements, especially if you have "normal" and not very fine ("needle") multimeter probes.)




  The computer was running very slowly and unstable. Someone suggested looking at the oscillator.


I'll just add that there are other possible causes of an old computer being unstable. The main crystal wouldn't be one of my first suspects. Connections (e.g. socketed ICs) are one area of concern. One of the main components which deteriorates with age, are electrolytic capacitors. Therefore I would include checking the quality of the power rail voltages with an oscilloscope, as the first part of any investigation.

A multimeter can measure "gross" problems on power rails, but is not able to show relatively "subtle" problems e.g. excessive ripple. In other words: If the multimeter shows there's a problem, then there is a problem; if the multimeter doesn't show a problem, there might still be a problem. Only an oscilloscope can show some types of problem.

You might want to visit the Retrocomputing Stack for specialist advice.