The best way to check the cables is to measure the voltage drop across the cable while the starter is engaged. Put your voltmeter on a low-volt range (say, 3V or whatever range is close), and put one meter lead at each end of the cable (jamb probe between insulation and the copper strands, that usually works).
Then have a helper crank the starter and see what the voltage drop across the cable is. Ideally you want zero, but realistically, you should see much less than a volt drop per each cable section, say less than 0.5V.
You can also measure the battery voltage directly across the battery while cranking (probably between 9-11 volts), and then move the positive meter lead down to the terminal right on the starter (also while cranking) and then subtract the two readings--the difference is the voltage drop across your battery cable.
As you found out while the starter was stuck (did it short out? Kind of sounds like it may have), cables can get really hot, especially if there are any high-resistance spots such as the crimps on the ends.
On my SD22, I put beefy battery cables on it, I think they were 2 gauge copper. The stock ground cable was, putting it nicely, crap! You want the ground cable going right from the battery to somewhere on the engine (I used a bellhousing bolt on the right side of the engine) to minimize the resistance in the circuit.
And if you don't have a voltmeter to test the cables, just use your hand and check for hot spots. If you crank for 5-10 seconds and then stop, you should be able to hold your hand along any point on the wires. If you can't--there is a problem, too much resistance.
HTH!
