Oshoala was the highest goal scorer at the 2014 FIFA U-20 Women's World Cup and was named the best player at the tournament.

She was also named the best player and second highest goal scorer with the Super Falcons team who won the 2014 African Women's Championship.

In July 2023, after her group stage heroics against Australia in the 2023 FIFA Women's World Cup, Oshoala saw a massive increase in her Instagram followership which made her become the first African female footballer to have a million followers on the social media platform.

[12] Despite missing two months of the 2015 season with a knee injury,[13] Oshoala scored three goals in the nine games in which she played as defending champions Liverpool finished in seventh place.

[17][18] In January 2016, Liverpool reported that a transfer bid from Arsenal had activated the release clause in Oshoala's contract and that she was discussing personal terms with the London club.

[21] Arsenal manager, Pedro Losa said of her signing, "Asisat is a fantastic talent and will be a great addition to our squad.

[27] The same year, she scored four goals during the 2017 Women's Super Cup and helped the club defeat Shanghai 5–3 to win the championship.

[28] On 31 January 2019, Spanish club FC Barcelona Femení signed Oshoala on a loan deal until the end of the season.

[36] Oshoala scored the game-opening goal in the fourth minute of the 2019–20 Copa de la Reina semi-finals against Seville.

[38] On 21 August 2020, Oshoala provided the assist for Kheira Hamraoui's game-winning goal in the 2019–20 UEFA Women's Champions League quarter-final against Atlético Madrid lifting Barcelona to the semi-final.

[39] On 24 March 2021, Oshoala scored the game-winning goal in the team's 3–0 win over Manchester City during the first leg of the 2020–21 UEFA Women's Champions League quarterfinals.

[40] On 16 May 2021, Oshoala became the first African woman to win the UEFA Champions League, after coming on in the 71st minute of the finals with Barcelona defeating Chelsea 4–0.

[41] During her time at Barcelona, Oshoala made 162 appearances and scored 117 goals, becoming the fourth highest goalscorer in the club's history and won 14 trophies which included two trebles.

[48] Oshoala's club coach Edwin Okon was serving as the national team interim manager when he gave her a debut senior cap in a friendly defeat by world champions Japan in September 2013.

[49] Oshoala was named as the best player at the 2014 FIFA U-20 Women's World Cup and was the top goalscorer at the tournament with seven goals.

She was also named best player and second top goalscorer with the Super Falcons team who won the 2014 African Women's Championship.

[59] Nigeria finished third in Group A and advanced to the knockout stages where they faced two-time champions Germany and were defeated 3–0 in a controversial match heavily influenced by video assistant referee (VAR).