You have to use 'overseas' rather than 'abroad' before a noun. For example, you can say 'an overseas agency' (but you can't say 'an abroad agency').

I have always considered the two to be interchangeable, but I am in the US, so to go 'abroad' I have to also go 'overseas'. If a person were from Europe, and traveling throughout all of the various European countries, one would be 'abroad', however, if they traveled to America or Australia, they would be 'overseas', because they crossed an ocean in their travels.

When there is a sea between you! :-) For example, if I live in France then my neighbouring country Spain is abroad but not overseas.

They are both interchangeable at times, but "overseas" sounds a bit old-fashioned, at least in American English. "Overseas" is usually used as an adjective (i.e overseas employment), but you can say (employment abroad) as well.