The "typeless" type, achieved by having a pure Fire-type use Burn Up, obviously has no weaknesses.
You can use the dual type chart on this site to see all the dual typings and how they stack up. In particular, the left column has a list of the combos that only have one weakness. In the case of pure Electric or Poison/Dark, that weakness is Ground, which can be patched out with Levitate or an Air Balloon. Bug/Steel's sole weakness is Fire, which can be negated with Flash Fire or Primordial Sea, while Water/Ground's is Grass which can be negated with Sap Sipper. The weaknesses for pure Normal (Fighting), Normal/Ghost (Dark), and Dark/Ghost (Fairy) cannot be negated except by the one-time reprieve of type-reduction berries like the Colbur, which still allows them to hit for normal damage. There is no ability (or item, for that matter) that can negate two or more entire types of moves at once except Wonder Guard, which doesn't do anything about types you're already weak to, so only the 1-weakness types need to be considered.
Triple-type combos can also exist, but current move mechanics dictate that at least one of these types must be either Grass (Forest's Curse) or Ghost (Trick-or-Treat), as those are the only two moves in existence whose function is to add a type. Out of the one-weakness combinations you can form with those moves, the only ones where that weakness is on a nullifiable type are Poison/Dark + Trick-or-Treat (where the weakness is to Ground, just like regular Poison/Dark) or Steel/Fairy + Forest's Curse (weak to Fire, and thus beatable with Flash Fire).