No self-combos that I'm aware of. Not like the commando neutron stomp & backbreaker combo you mentioned, which I find awfully nice and useful.

And I'm pretty sure I would've noticed if my skills caused a combo and they haven't, so if there is one then one of the following skills that I don't have would have to play a part in it: (auto attack) suppression, (no)protection, mana bubble or sonic boob.

As for inter class combos, the op skill psychic lash combos with a follow-up transference, not all ops have/use it though.

The suppression combos with the commando force hammer, but even fewer engineers have suppression (and for good reasons, never mind the few stray dogs that speak some mumbo jumbo you about suppression, protection, incinerator and about this weird "support engineer" concept).