The first theme, Be Loud, focuses on Birmingham’s activism, community spirit and musical heritage, organisers said.
Objects include a 1950s portable record player, an Honor melodeon donated by Irish musician, Pat Brennan, and material connected to Birmingham-based Oriental Star Agencies record label.
There are also 1962 membership cards for the Tudor Dance & Social Club at the Locarno dance hall in Hurst Street.
The gallery explores the communities and businesses that helped shape the city, including its curry house history.
A recreated table setting from the Koh-I-Noor curry house recalls one of Birmingham’s earliest curry houses, which opened on Horse Fair in the 1960s.
Artist and curator, Mohammed Ali, saved parts of the restaurant including original partitions and unused rolls of wallpaper, when the building was being renovated.
The Play Hard section looks at Birmingham’s sporting history, with objects including boots and a mouthguard donated by Birmingham-born bare-knuckle boxer, Melanie Shah, skates belonging to speed skater, Eric Grinsell, and a Small Heath Harriers running shirt.
It also features Chad Valley toys made in Birmingham between the 1950s and 1970s, and a vintage Cluedo game.
Cluedo was invented in Birmingham during the Second World War by Anthony Pratt. His wife, Elva, also helped design the board.
The Make Change element tells the story of the Citizens’ Jury in the jurors’ own words and explores the impact of their work.
The Citizens’ Jury was the first of its kind to take place in a UK museum.
It was supported by the National Lottery Heritage Fund and facilitated by Shared Future.
Wajid and Mensah added: “We hope visitors will help us build on Birmingham’s story by sharing their own memories, knowledge and experiences. Museums don’t have to be the final word on history – they can be places where stories continue to grow.”