Jane Byrne, a controversial and outspoken protege of the late mayor Richard J. Daley, will run for mayor next year as an alternative to what she calls "a cabal of evil men" who took over the city government when Daley died in 1976.

her candidacy introduces excitement into a Chicago mayoral election for the first time since Daley rose to power more than two decades ago. Byrne is a former City Hall insider - the first to break the code of silence about what goes on in the last big city political machine in the country.

"This is like taking on Hercules," Byrne, 43, the daughter of a wealthy steel executive, said in an interview last week, "but I can win because the people are sick and tired of paying the price of corruption. City inspectors are taking bribes all over the place. City Hall has become a place of oppression and hostility to the ordinary citizens of Chicago - to those who have no clout."

After announcing her candidacy last week she opened headquarters across the street from the Federal Building, where a grand jury is investigating her charges that Mayor Michael A. Bilandic "greased" the way for a 1977 taxi fare increase.

Byrne was Daley's consumer sales commissioner and the first women to serve in the mayor's cabinet - a job from which she was fired by Bilandic after she went to a local television commentator last November with charges that she heard Bilandic advise cab company executives to alter financial records to justify the fare increase.

"Taxigate' is just one example of corruption at City Hall," Byrne said. To end it, you have to shake the whole tree. You have to be prepared for an awful lot of trouble. When I found corruption I would go straight to the U.S. Attorney. I would put patronage aside, and the ones who are corrupt would have to go."

She also charges that the "cabal of evil men" at City Hall - including the mayor and at least two aldermen, Edward R. Vrdolyak and Edward M. Burke - has set wrong priorities, such as planning a new sports stadium when the city needs a new central library. Also, she says, schools are starved for money and neighborhood streets are full of potholes. And she promises to dismantle the Chicago police intelligence division, which has complied massive "political files" on hundreds of Chicagoans never suspected of crimincal activity.

Byrne's critics, however, find a hollow ring in her talk about "evils" of a political machine that she had been part of for years without complaint. She did not say a word publicly about corruption during Daley's last five years, when scores of local officials and police officers were indicted and convicted on federal charges.

In announcing last week, Byrne became the first of four or five candidates expected to enter the primary election race against Bilandic, 49, who is an unannounced but almost certain to seek reelection.

Martin J. Oberman, an independent Democrat and loney foe of Bilandic on the City Council, said, "I don't think she has a realistic chance. But if there are other serious candidates, she has the potential to keep Bilandic on the offensive. As a former insider, she's going to hit him where she knows it hurts. He's not going to be able to talk about the wonderful city, because he's going to be defending himself."