Ahead of a run of four games in eight days, the Brazil international says Rafael Benitez's men will treat every competition equally and attempt to win all their matches.
The Blues travel to Southampton on Saturday looking to keep their top-four hopes on track, before hosting Manchester United on Easter Monday in the FA Cup sixth round.
Rafa Benitez's men then face Rubin Kazan in the Europa League last-16 three days later and, finally, a league meeting with Sunderland on Sunday.
The 21-year-old admits it is unusual to face such a congested fixture list, but is keen for the west London club to aim for victory in every game.
"There are so many games at the moment, and all of them are important. We have Southampton first and then Manchester United 48 hours later," Oscar told reporters. "But that is the way it always is at a club like Chelsea. We always have a lot of games, though maybe four in a week - as we have this week - is a bit different."
He added, "We have to play and rest as best we can. It is a week that could be really important for our season. We have games in all three remaining competitions, but we're not thinking that one could be more important than the other. We want to win all of the games and we want to do as well as we can in all the competitions. We won't sacrifice one for the others."