Avdija was born in kibbutz Beit Zera, Israel. His father, Zufer Avdija, is a Serbian-Israeli, from a Muslim-Gorani family (from Kosovo), and he is a former professional basketball player who played in Israel in the '90s. Zufer was the team captain of the Serbian powerhouse Crvena zvezda in 1980s and a member of the Yugoslavia national team that won the bronze medal at the 1982 FIBA World Championship. Deni's mother Sharon Artzi is an Israeli Jew.
He started playing basketball when he was 8 years old. Avdija played for Bnei Herzliya youth team and later joined Maccabi Tel Aviv youth team in 2013. Avdija led Maccabi to three consecutive youth state championships from 2017 to 2019.
In November 2017, Avdija started his professional career with Maccabi Tel Aviv, signing a six-year deal. On November 19, 2017, Avdija made his professional debut in a match against Ironi Nes Ziona, Avdija played three minutes and became the youngest player ever to play for Maccabi at age 16 years, 320 days.
In July 2018, Avdija was a member of the Israeli Under-20 team that won the gold medal at the 2018 FIBA Europe Under-20 Championship. He averaged 12.7 points, 6.4 rebounds, 1.1 assists and 1.3 steals per game. Avdija earned a spot in the All-Tournament Team, alongside his teammate Yovel Zoosman.
In August 2018, Avdija participated at the Basketball Without Borders Europe camp in Belgrade, Serbia and was named the camp MVP. In February 2019, Avdija participated at the NBA All-Star Basketball Without Borders Global Camp in Charlotte, North Carolina and came away with camp MVP honours. Avdija was selected to the all-tournament team for the 2018–19 season of the Next Generation Tournament. He dominated the proceedings by leading the tournament in scoring with 24.7 points per game, rebounds (12.0) and performance index rating (29.7). He was also ranked second in assists (6.7) and fifth in steals (1.7).
On February 21, 2019, Avdija made his debut for the Israeli senior national team in an 81–77 win over Germany.
In July 2019, Avdija led the Israeli Under-20 team to win the 2019 FIBA Europe Under-20 Championship, winning the gold medal for two consecutive years. Avdija was named the Tournament MVP after scoring 26 points, 11 rebounds and 5 steals against France and 23 points, 7 assists and 5 rebounds against Spain to lead the team to its victories.