Two converging confusions seem to beset you:
- Gerunds are confusing because they behave like nouns and verbs. They can take an object like a verb, but they fill a place in the sentence like a noun:
A gerund behaves as a verb within a clause (so that it may be modified
by an adverb or have an object); but the resulting clause as a whole
(sometimes consisting of only one word, the gerund itself) functions
as a noun within the larger sentence.
In the sentence, the phrase: inviting Steve and me to your home for the birthday celebration, is the object of the preposition for.
Inviting is the gerund verb of the phrase, while Steve and me is the object of the gerund.
- The real issue is the compound object of the verb: Me is the correct expression for the direct object, and this simple test confirms its correctness, when you eliminate the first object:
Thank you for inviting me to your home for the birthday celebration.
Adding Steve again:
Thank you for inviting Steve and me to your home for the birthday celebration.