Hello,
Am an international student currently on an F1 student visa in usa. Can I tutor students off campus or is it illegal to do that on my current visa status? If I can tutor, should I collect payments in cash only?
Thanks.

How you accept payment is irrelevent; you are technically working and earning money in violation of your visa, but...

It is only a minor violation and will be tolerated, provided your income is not TOO high (say, not in excess of $10,000) AND provided you file Schedule C and pay the required state and federal INCOME taxes by filing Form 1040NR. You are NOT liable for self-employement taxes due to your international student status.