Colloquially, you'll mostly hear "Tiefkühler" or "Gefrierschrank", because, as Dirk says, you won't often find the huge, coffin-like devices ("Gefriertruhe/n" or "Tiefkühltruhen") in private homes anymore.

I've only heard "Vereisungsgerät" in a medical context, and I very much doubt it's used to store food. :-) But I suppose such a device would also be called "freezer" in English. For the ice-cold food storage device, you use "Tiefkühlschrank" or "Gefrierschrank" ("fridge/refridgerator" is "Kühlschrank"). The very large ones that don't stand upright and have a door, but do have a kind of lid, are called "-truhe" instead of "-schrank", but you normally won't find them in a home.