Can a regular refrigerator be stored for a few months on its side? Will this cause any damage?

No do not store on its side! Yes it can cause damage. Oil will drain out of the compressor and if all doesn't run back in it will burn up the compressor. Also when storing for a period, leave the doors cracked for air circulation to prevent mold build up and that old musty smell that is hard to get rid of.

How about just moving it, say a 30 min truck ride to the other side of town?

How about just moving it, say a 30 min truck ride to the other side of town ??

I don't understand the answer to laying it on its side