Ogedi-Uzokwe was a member of the youth teams at two English Football League clubs, Leyton Orient and Millwall, separated by a spell at Ilford. He made the step up to men's football at Enfield 1893 at the age of 18. In late 2013, he signed for Aveley before moving to Nottingham and signing for Hucknall Town and Carlton Town. He returned south to play for Hayes & Yeading United, Barkingside and Lewes.
Türk Ocağı Limasol
On 26 January 2016, Ogedi-Uzokwe joined Northern Cypriot club Türk Ocağı Limasol. He made his debut the following day in a 2–0 victory against Gençli̇k Gücü in the Cypriot Cup Second Round first leg. On 31 January, Ogedi-Uzokwe scored his first goal for the club in the 7–0 second leg victory. After going four games without a goal, he scored both goals in a 2–0 win at Yeni̇cami AK on 5 March. Ogedi-Uzokwe scored his first goal of the season two weeks later in a 3–1 win against Bostanci Bağcil. In September 2016, Ogedi-Uzokwe returned to the club for a second season but went seven games without a goal. He eventually scored in a 1–0 win against Küçük Kaymakli on 13 November. His second goal came a month later when opening the scoring of a 2–0 win against Gençli̇k Gücü on 30 December. Following a further 14 goalless games for Ogedi-Uzokwe, mostly because he was playing as a midfielder, he scored three goals in April to seal league victories against Çetinkaya Türk and Ci̇hangi̇r. Having appeared in every match of the 2016–17 league campaign, Ogedi-Uzokwe scored twice on the final day of the season in a 6–2 win against Gençli̇k Gücü. A week later, he played 89 minutes in a 1–0 victory against Yalova in the Cypriot Cup Final to celebrate his first piece of silverware with the club.
Maldon & Tiptree
In July 2017, Ogedi-Uzokwe joined Isthmian League North Division club Maldon & Tiptree upon his return to England. He made his debut in a 1–0 win at Ware on 12 August, and scored his first and second goals for the club a week later in a 5–1 win against Waltham Abbey on his home debut. In September 2017, Ogedi-Uzokwe scored 10 goals in just eight games, including a hat-trick in a 4–2 win against Tilbury. The following month, he scored eight goals in seven games. During his goalscoring run, he scored in nine consecutive games from 23 September to 28 October, and scored in 15 consecutive league games between 9 September and 2 December. On 25 November, he scored his second hat-trick of the season in a 5–1 win versus Dereham Town. On 1 January 2018, Ogedi-Uzokwe marked his final appearance for the club with a 90th-minute winner against Witham Town. He scored both goals in the 2–1 victory. He left the club having scored 34 goals in 34 games in all competitions.
Colchester United
On 3 January 2018, Ogedi-Uzokwe joined League Two club Colchester United alongside Maldon & Tiptree teammate Ryan Gondoh. He signed an 18-month deal. He made his professional debut for Colchester on 20 January 2018 as an injury time substitute in their 1–1 draw with Grimsby Town. He then scored his first professional goal on his first start for the club from the penalty spot, before turning provider for Mikael Mandron in Colchester's 2–1 win against Coventry City on 13 February. After nine appearances in the 2017–18 season, he vowed to return stronger for Colchester after a full pre-season with the club.
Bromley loan
On 27 July 2018, National League side Bromley signed Ogedi-Uzokwe on loan until January 2019. He made his Bromley debut as a second-half substitute in their 2–1 defeat at AFC Fylde on 4 August. He scored his first goal for the club with an 88th-minute winner in a 1–0 win over Gateshead on 18 August.
Derry City loan
On 7 February 2019, Ogedi-Uzokwe joined League of Ireland Premier Division side Derry City on loan until 30 June. He made his debut on 15 February in Derry's 3–0 win against UCD. He scored his first goal for the club in a 3–0 win in the League of Ireland Cup against Longford Town on 2 April. His loan was extended to the end of the League of Ireland season after an automatic one-year contract extension was activated by Colchester. Junior finished the season with 16 goals and 11 assists in all competition. Finishing as the league's top scorer with 14 goals.
Hapoel Hadera
On 5 February, Colchester United announced the departure of Ogedi-Uzokwe to Israeli Premier League side Hapoel Hadera on a permanent contract. He made his debut for the club the same day, starting in a 1–0 win against Bnei Yehuda.
