"Tapadh leibh" pronounced "tappa lave" - if you are speaking to more than 1 person or want to be politeIrish Gaelic:Irish does not have the informal/formal distinction as in Scottish Gaelic.
"Go raibh maith agat" (gurra mah aggut) - singular
"Go raibh maith agaibh" (gurra mah oggiv) - plural
Irish Gaelic: Go raibh míle maith agat. (A thousand thanks) in Irish.
I've seen all of these used for Scottish Gaelic
Scottish Gaelic (Scotland) Tapadh leat
Scottish Gaelic (Scotland) [formal] Tapadh leibh
Scottish Gaelic (Scotland) [many thanks] Moran taing
Scottish Gaelic (Southern Scotland) [for.] Gu'n robh math agaibh
Scottish Gaelic (Southern Scotland) [inf.] Gu'n robh math agad
Though the last two are a bit antiquated
I have yet to see literally "Thank you, very much" though
In Irish it's: Go raibh maith agat (singular) / Go raibh maith agaibh (singular)
In Scots Gaelic: Tapaidh leat/Tapaidh leibh.
Go raibh maith 'ad/agaibh (plural)
(Guh ruh mah ad/ah-gee) hard 'g' as in gate
Irish Gaelic: Go raibh maith agat (singular)
Scottish Gaelic: móran taing!
gun robh math agad!
Scottish Gaelic: 'S e do bheatha.
Manx Gaelic: She dty vea.
Irish Gaelic: Tá fáilte romhat.
In Scottish Gaelic thank you is tapadh leibh Pronounced "tahpæ leyv"
Go raibh maith agat, a stóirín.
In Irish you might say 'Táim buíoch díot faoin leabhar'. (I am grateful to you for the book). In Scottish Gaelic: ?
Go raibh maith agat, a ghrá.
thanks for all the birthday wishes
Go raibh maith agat (to one person only).
In Irish it's "go raibh maith agat as an gcluiche fichille
Go raibh maith agat as cur meangadh uirthi
'Thanks be to God" = Buíochas le Dia.'Thank you' = Go raibh maith agat.
In Irish it's "Go raibh maith agaibh as ucht cluas a thabhairt dom"