Dual Canadian / Irish Citizen moving to the UK

can I enter using my Irish passport through the EU line?

As an Irish citizen you have an absolute right to enter the UK, in fact more so than other EU citizens. So they cannot refuse you, full stop, regardless of what the passenger manifest looks like.

In any case, you should check in using the Irish passport (although in the case of Canada, airline staff may want your Canadian passport as well, since Canada does not do exit border checks). As a rule of thumb, you should use the passport to be used for the destination country.

Canada does not not check passports on exit (at last not at airport). You will not need to show any passport to Canadian authorities when you leave. You will need to show a passport to the airline.

The only important point is that you need to show your Irish passport to UK immigration on entry. Canadians are allowed to enter the UK without visa, but if they ask you why you are coming to the UK and you say "to live there" they will need proof that you are allowed to do so. Your Irish passport gives you that permission. Your Canadian one does not. Your Irish passport also allows you to use the EU line.

You also need to present a passport to the airline to prove that you are allowed to enter the UK. It doesn't matter which one you choose, since both Canadian and Irish can enter the UK without a visa, and the airline will neither ask nor care what your purpose in coming to the UK is. Using your Irish passport is probably marginally simpler, but there is no problem with giving a different passport to the airline from the one you will be entering the UK on. make sure you have both available of course.