The thread title said evil or unlikeable. Because Sweeney and Lovett are both evil, I think it satisfies the OP's conditions.
(edit: post above is edited lol I guess you realised this before I posted)
"You can't overrate Bernadette Peters. She is such a genius. There's a moment in "Too Many Mornings" and Bernadette doing 'I wore green the last time' - It's a voice that is just already given up - it is so sorrowful. Tragic. You can see from that moment the show is going to be headed into such dark territory and it hinges on this tiny throwaway moment of the voice." - Ben Brantley (2022)
"Bernadette's whole, stunning performance [as Rose in Gypsy] galvanized the actors capable of letting loose with her. Bernadette's Rose did take its rightful place, but too late, and unseen by too many who should have seen it" Arthur Laurents (2009)
"Sondheim's own favorite star performances? [Bernadette] Peters in ''Sunday in the Park,'' Lansbury in ''Sweeney Todd'' and ''obviously, Ethel was thrilling in 'Gypsy.'' Nytimes, 2000
So does this mean like characters that you are not supposed to like but they really do a great job of being a villain so they get awarded for it? Because it's really cool I think. Characters you love to hate
You could make a case for the ladies who've won playing Rose Havoc. She is after all the stage mother from hell... Dorothy Loudon as Miss Hannigan, Patti LuPone as Eva Peron, Bebe Neuwirth as Velma Kelly. The characters aren't evil per say, but do indulge in questionable activities: child abuse, political corruption, double homicide...
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body
Well, many of the greatest roles out there are villain/antihero characters, or at least characters with great flaws. Whether someone kills and eats people like Hannibal Lecter or is a cheating husband and overbearing father like Willy Loman, if you think about it, human failings are the foundation of drama.
Since you've defined the question so broadly and to include anti-heros and seriously flawed characters (who could argue that Billy Flynn isn't a seriously flawed human being?), many, just looking at the guys:
(note, of course, that many of these are of the musical comedy lovable bad guy, heavy, or pain in the butt type; others are nobly anti-heroic and driven; one or two are down and out nasty guys)
Ray Walston in Damn Yankees Jonathan Pryce in Miss Saigon Norbert Leo Butz Dirty Rotten Scoundrels John Lithgow The Sweet Smell of Success Bert Lahr in Foxy Ben Harney in Dreamgirls James Naughton in Chicago Brent Carver Kiss of the Spider Woman Len Cariou in Sweeney Todd Barry Bostwick in The Robber Bridegroom (at least the Robber part of the title role)
featured:
Myron McCormick in South Pacific Yul Brynner in The King and I Cyril Richard in Peter Pan David Burns in The Music Man Jack Cassidy in She Loves Me Hiram Sherman in How Now Down Jones Rene Auberjonois in Coco Keene Curtis in The Rothschids (some of his roles) Henderson Forsythe in The Best Little Whorehouse in Texas Chuck Cooper in The Life Shuler Hensley in Oklahoma Chuck Cooper in The Life
Some odd choices here. Though arguable, I'd add Owen Teale for A Doll's House. One of the most perfect productions of a play I've ever seen. And we may be adding Bertie Carvel to the list next year.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian