Philadelphia's museums, pools, libraries and offices reopened yesterday after a 20-day strike collapsed and employes returned to work without a contract. Meanwhile, Detroit officials said they would ask an appeals court to declare a strike by 7,000 city workers illegal.

City supervisors in Detroit worked overtime to keep critical departments open during the strike, which began Wednesday over wages. About 5,000 nonunion workers have honored picket lines in the nation's sixth-largest city. "From food inspection to drinking water, the fact that these people are not here can cause untold problems," said Donald Pailen, a lawyer for the city.

In Pittsburgh, a strike by 300 unionized garbage collectors was averted late last night when the city and Teamsters Local 609 agreed to continue negotiations while extending for the 10th time the current contract, which expired Dec. 31.

Philadelphia's garbage haulers, who began working Saturday under court order, continued to remove more than 40,000 tons of trash dumped in legal and illegal sites by the 1.7 million residents of the nation's fifth-largest city. The 12,884-member District Council 33 of the American Federation of State, County and Municipal Employees voted Sunday to return to work.

Some returning workers were unhappy, blaming District Council 47, the white-collar union whose members crossed picket lines, and the judicial order that forced trash collectors back to work. But Mayor W. Wilson Goode said District Council 33, the blue-collar union, has the city's "last and best" offer -- a 10 percent wage increase in a two-year contract accepted by District 47.