Can I use the Oyster Card for the Heathrow Express to travel to London??
No. The Heathrow Express is run by the airport and only accepts its own tickets.
Oyster Cards are accepted on the slower commuter trains between Heathrow and Paddington that stop at all stations, and on the tube (Piccadilly line). Depending on where you are going in London, the time advantage of the Heathrow Express may be used up in getting from Paddington to your final destination.
. . . and Oyster Card. I have received them in the mail and will have them in hand when I land at Heathrow.
Not sure what you mean here by "hand them in". You use the Oyster card to get through the turnstiles at your start and end station (or when you get on a bus), and it calculates the correct fare and docks that from the total on your card.