You will get a job in China easily, nobody will check on your criminal record, China is full of people from the West who have criminal records.

If you want to teach at a university you will need a degree, and possibly a TESOL certificate, however it is easy to get a fake TEFL/TESOL certificate, and they are cheap.

China is your best bet, you will have no problem. Korea and also Vietnam REALLY DO carry out criminal background checks, or they at least were up until recently.