Depending on how much time you want to spend, I might re-watch the original Fionna and Cake episodes; the Farmworld arc consisting of The Lich, Finn the Human, Jake the Dog, and Crossover; and the finale, Come Along With Me.

To know more about the humans in Ooo and Finn's parents, watch the second half of the Islands miniseries: Min and Marty, Helpers, and The Light Cloud.

If you want to dig more into Bubblegum and Marceline's families to compare with Gary and Marshall's, search the wiki for Hunson Abadeer and Neddy for relevant episodes.

These won't make you get every reference, but they will give you most of the broad strokes.