Arsenal host Sporting in tonight's Europa League last-16 decider, following a 2-2 draw in Portugal last week, before aiming to extend their five-point lead at the top of the table in Sunday's visit of Crystal Palace.
On Monday, Odegaard was named Player of the Year at the London Football Awards as Arsenal became the first ever club to complete a clean sweep of the four top gongs, with Mikel Arteta (Manager of the Year), Bukayo Saka (Young Player) and Aaron Ramsdale (Goalkeeper) also recognised.
Arteta has targeted winning both competitions and the captain believes the January additions of Leandro Trossard, Jorginho and Jakub Kiwior, who made his debut in Lisbon, have given them the squad to compete on an extra front.
Asked if Arsenal can win the Europa League and maintain their League form, Odegaard told Standard Sport: "Yes. The last transfer window was really great. The additions have really given a lot to the team in terms of different qualities. Also off the pitch, for example Jorginho is an experienced guy who has won a lot of things. They all look great and are great additions to the squad. You saw the other day [in Lisbon] they're all great players.
"When they came into the team, I think they felt part of the squad and the family from day one. It's the way this club is. That's what good about this team, we're so connected and we make everyone adapt quickly. That's what we did with the new signings too."
He added: "We want to win every game, we want to win everything we're part of. We're going to fight to win everything we can.
"We've said it many times, so it sounds like a cliche, but it's actually true that we take it game by game. That's what we've done the whole season. That's what we're going to keep doing. Just focus on every game, every training session: how we can improve every day."
Odegaard missed the first leg through illness but could return to the XI tonight, although summer signing Fabio Vieira impressed on his return to Portugal.
"We see every day in training the quality he has," Odegaard said of the 22-year-old. "He's an unbelievable player. That's true of a lot of the players who aren't playing at the moment. You don't see every day how good they are but we see it, the quality they have and how much they can offer to the team. That's one of the hardest things about football, you can only play 11."
Odegaard's Player of the Year award is recognition of the Norwegian's standout season and he praised Arteta for taking his game to a new level.
"It's the way he [Arteta] looks at football, the details he sees," Odegaard said. "So many things you don't even think about then he tells you this, you do it and you see how it works! There's just so many details in the game that he sees and no-one else I've met sees. He's great.
"I think the main thing [Arteta has improved] for me is the position in attack, how to be a threat, to be more dangerous and come into the right areas, what zones to attack and when to create things.
"When he speaks, you just know this is a good man and he knows what he's talking about. I just had this feeling with him straight away."