What affect do you think this group might have had Roman culture when they migrated

I'm guessing you mean on Roman culture.

In that case, the Romans have witnessed the migration of several tribes. What was once a mostly Roman-based empire, where the majority of people who lived there were born on the area of modern day Italy, the more Roman influence expanded, the more their empire included different ribes with drastically different cultures. The main effect each of these cultures had on Roman culture was the intermixing and value sharing which intermixed Roman culture with theirs. This made actual and "original" Roman culture less different from the one of different tribes that have lived with them in their empire.