The usual word for a meal in Irish is béile, which is masculine. A quite full synonym is séire, another masculine. There is also proinn, a feminine word, but I don’t recall ever seeing it in folklore.
Breakfast is usually bricfeasta, with many dialectal parallel forms – one of the most distinctive being briocast, which I have seen in folklore texts from the Ring of Waterford. You can also use céadphroinn (from c(h)éad- “first” and proinn), but this word reeks somewhat of officialese. Béile maidine “morning meal” is another possibility.
The English word “breakfast” comes from “breaking the fast” in the morning. This kind of morning fast is in Irish céalacan, and you can say céalacan a bhriseadh for “breaking the (morning) fast”. Céalacan has also been used in the sense of starving, and of hunger strike (although stailc ocrais is more common in that sense). Pictiúr an chéalacain or the “picture of the morning fast” is someone who is starving and looks that way.
Lunch is translated with lón, but note that it has a more general meaning of “supplies, provisions”. Lón léitheoireachta means basically a leisurely kind of reading, and lón cogaidh is ammunition. Another expression for “lunch” is béile meán lae (note that that meán part isn’t inflected here). The business of catering is very unsurprisingly called lónadóireacht, gnó na lónadóireachta.
For “supper” the English loanword suipéar is quite established, but obviously béile oíche can also be used.
The verb for “having” a meal is caith!/caitheamh. Of course, “eat” is ith!/ithe. When you have had enough, you can say tá mo dhóthain agam or tá mo sháith agam; the expression tá ceas orm is suggested by Mícheál Ó Siadhail in Learning Irish, but Niall Ó Dónaill’s dictionary says it means you have eaten too much.