[RiseofAsia]

Some people said must off mobile data when in overseas.
Others said must on....which is correct?

Think sensible to  off mobile....safer....to avoid unnecessary spillages which will incur charges.

Can the roam still work when mobile data is off?

Yes. It still can work.
Data roam is actually mobile data using another network. Mobile data normally for local use. You can switch it off and turn on data roam. If you scare off unnecessary charges coming from your background apps which probably did not do a proper switching.

Always remember dont open any sms you receive when you are oversea. It may incur additional charges.