Is expiation obligatory and is it considered a Ghamus oath for someone who nodded their head in falsehood to a person who swore them by Allah regarding a matter?

An oath is not constituted by merely nodding the head, so there is no expiation due upon you. However, you must repent to Allah Almighty for having answered the questioner's query untruthfully by nodding yes. A nod is considered speech in custom and language, and it is a form of indication.