Oyster card - worth it for a 3 night stay?

Yes, it is. With an Oyster Card you will never pay more than a bit less than the cost of a travelcard for the zones in which you travel each day. The Oyster computer will automatically give you the best fare which will be substantially less than single tickets. See the fares here. Yes, it will get you to Heathrow where you can get a refund of any unspent money you loaded on the card plus the deposit.

I assume you mean you are at the Gloucester Road tube stop.

Yes. You will need to use the tube. You are within walking distance of the South Kensington museums, but most of the other London sights will want to take the tube to ... otherwise you will spend all your time walking and none of your time actually seeing the sights. London is a big city.

Given how expensive London is to begin with, I personally think that use of the Tube is perhaps the biggest bargain there for a traveler. Since you want to maximize your sightseeing time and minimize the time walking, it is well worth the expense. Since you may not use it too much over those three days, the Oyster card makes much more sense than the Travelcard.

I just got back from a 4-day trip with my sister. We were staying by Hyde Park/Oxford St, and ended up using a combination of travel options. We purchased RT tickets on the Heathrow Express, which brought us to Paddington from the airport in 15 min. Then we ended up (a) doing a ton of walking, which was great. Awesome city for walking. (b) purchasing a day's pass from one of the tourist bus companies - we used the Original Bus Tour - which also included a trip on the Thames Clippers and (c) buying Oyster cards. The Oyster card is a good deal - there is a deposit you pay for the card, but I got mine refunded at Paddington on the way back to the airport very quickly and without fuss. We used it for both buses and the tube. The only reason I would advise buying the Heathrow Express ticket is because of how quickly it got us between the city and airport, and because it was our first trip to London, I didn't want to have to figure out where to switch routes on the tube and fight morning commuters after flying all night.

Have fun!

The OP is staying near Gloucester Road. This is a case where it is faster to take the tube than the Heathrow Express. It is only 40 minutes and you can use Oyster. If they took the Heathrow Express, it would take longer because they would still have to get from Paddington to Gloucester Road by tube or taxi.

My bad, thought it was a much quicker tube trip from Paddington to Gloucester Rd than it must be.

The tube ride from Paddington to Gloucester Road is under 15 minutes ... it is just once you add in the time waiting, transferring, etc., you eat up any time savings from the fast ride to Paddington. Because Gloucester Road is right on the Piccadilly line, the tube really is an easy option.

Thank you all for the good advice. I just returned home last night. While in London, we did indeed purchase the Oyster Card and were glad we did. It made travelling on the tube so easy, with not having to buy individual tickets. A real time saver! Redeeming the deposit and unused portion of the card was easy, too. Just used the assistance booth at the Heathrow terminal. My sister returned at Terminal 5, which I understand is the only tube station that doesn't have a booth for redeeming the Oyster Card, but she was able to redeem her card earlier and buy a single ticket to her terminal. We had a smashing stay in London!

Side question: We will be leaving via Eurostar. Is there a place within the station to turn my ticket back in like at Heathrow?

You would turn it in at Kings Cross St Pancras underground station.

The reason for T5 Heathrow being a bit unusual is because the underground station booking office is managed by Heathrow Express and not TfL. There are a handful of other oddities regarding Oyster refund availability at certain stations, but these are unlikely to affect visitors.