"Let's invite them to our home in Poland!"
Translation:Ni invitu ilin al nia hejmo en Pollando!
"ĉe nin", I think, because they are coming to our house. (Once they are there and are staying at our house, they will be "ĉe ni").
Accusative is only used after those prepositions that can indicate either movement or location, to show that it's the movement which is meant.
al (and ĝis and tra) always indicate movement, so they don't need to distinguish the two cases and so they always take the nominative case, as is the general rule with prepositions.