I inherited a set of dishes from a Jew.
I don't know how observant this Jew was.
Do I need to toivel them?
There's two issues going on here: tevila and hachshara.
Tevila is required for dishes bought from a non-Jew, to remove the impurity of the non-Jew (Prisha YD 120:2, Taz 120:1, Ben Ish Chai Matos 2:1, Kitzur Shulchan Aruch 37:1). This is learned from the war with Midyan, which, appropriately enough, was read outside of Eretz Yisrael this past week in Parshas Mattos. Because of this fact, tevilas keilim is thus a din d'Oraisa, and we pasken safek d'Oraisa l'chumra. So if you don't know if it's been toveled or not, go ahead and tovel it.
But if the previous owner wasn't observant, you may very well have ended up with a set of treif dishes. Because there are many different requirements for kashering - what can be kashered, how to kasher it, etc. (also learned from the war with Midyan) - I would advise you to CYLOR.