Does Strava display watts from a bluetooth power meter along with a bluetooth heart rate in real time while I'm riding?
Not with the free version — it displays a delayed average. If you sign up for the premium program you get real-time, live monitoring.
What you can do to get live Watts is to use another program (for example the one provided by your wattmeter) to record and view your data live — then export the track to strava after the fact.
As an update - in October 2019 Strava disabled direct peering/pairing with sensors, and claimed it was a significant source of instability within the phone-based app. So your directly-connected heart-rate strap, power meter, or cadence sensor stopped reading to a phone. These devices still report through a head unit though.
So if you have sensors and only a phone, there is no external data available anymore, and any power figures will be estimated only.
In May 2020 Strava announced significant reductions on what the free user can see.
So even with a head unit and sensors, you can't analyse your sensor data through the phone app. You can see your speed and estimated power over the whole event, and that's it. You can't see per-segment data.