Can I travel to Thailland/China, with a Irish passport, that will expire in 3 months, only going for 2 weeks?

well i suppose you could try but general requirements stated by the thai embassy require your passport to be valid at least 6 months before expiration date, this is usually a general requirement for all countries as they could take this as a foreigner who might try to stay in their country also, be aware you will need a visa for china if you dont have one already, only people of hong kong may go to china visa free

Your passport cannot expire within six months of your entering Thailand or China. This is the rule in most countries (at least, the ones I have visited). Even if you are only going for 2 weeks, you will need to renew your passport first (and if you are in the US, that could take a LONG time so I recommend you renew your passport early).