"Bhí sé ag insint dom."

Translation: He was telling me.

[smrch]

This is an odd statement. Where's the object?

[Matthewdk14]

there is none, it is implied. Dom is an indirect object "to me". But we have know idea WHAT he was telling me. Probably it is a reference to a previous sentence.
You know that Paul is now the President?
Yeah, he was telling me...

[deserttitan]

Is it more common in Irish to use the phrase "He was telling me" than "He was saying to me"? Which the latter is what I'm more used to saying in English.

[galaxyrocker]

My idiolect would definitely use "He was telling me" more than "He was saying to me." In fact, the latter sounds distinctly 'weird' to me. Though the former would generally have something else with it, of course.

[FeargalMcGovern]

is this the same as "he told me"?

[galaxyrocker]

No. That'd be D'inis sé dhom

[Matthewdk14]

dhom? why not dom?