Heathrow to central London at night (with teens)

The cheapest way is by London Underground Piccadilly Line. Last train from Heathrow is at 0021 from Terminal 1-3, 0009 from T4, and 0018 from T5. If you're any later than that there's a cheap but very slow London bus route N9, or taxis.

Christine.

what time does the plane get in?

by "Paddington Line" do you mean "Piccadilly Line"? There is no Paddington Line. Paddington is on the District Line, Circle Line and Hammersmith and City Line.

I repeat my question with slightly different words - how late is late? And a followup question: how many teens?

There's a fair chance that a prebooked Private Car hire may well end up cheapest per person, most convenient and maybe easiest. But not necessarily.