Sol Badguy: His real name, (Frederick) last name, (a reference to "Mr. Badguy") and even his theme song ("Keep Yourself Alive") are some of all the references to Freddie Mercury and Queen in general (to hammer the point home, his head-plate has the words "ROCK YOU" engraved on it). It helps that hisVA (Daisuke Ishiwatari, also the man behind the game) is a huge fan of Queen, something you'll see in this entire page.
A relatively subtle one—his sword technique is clearly inspired by Mercury's theatrics with the top half of a mic stand.
Slayer in and of himself seems to be a nod toward Ozzy Osbourne, being the series most powerful and influential character. It also helps that his wife is also named Sharon.
He's also a massive homage to two characters from Giant Robo, Chief Chujo and Shocking Alberto.
Also, several of his stuff is inspired by Led Zeppelin, such as his theme song ("Burly Heart") sounding very "Kashmir"-like the name of his nation being Zepp.
His fist attack is called "Hammer Fall", both a reference to the Queen's song "Hammer To Fall" and the Power Metal band of the same name.
Coincidentally he has blonde hair, wears sunglasses and is quite a flirt much like Johnny Bravo
Johnny also has some clear parallels with Zorro. The black clothes, the bandit style, the swordsmanship - it's all there. Heck, one of his Overdrives even inflicts a Zorro Mark on his opponent!
A.B.A., a Canon Immigrant from Isuka. Her name is clearly a reference to the swedish pop group ABBA, as well as to ternary form in music.
Kind of a long shot, but A.B.A.'s key companion, Paracelsus, could have some inspiration from the band Laibach's side-project album Paracelsus.
I-No's character design is based off of Japanese rock singer Shiina Ringo, complete with her trademark mole {which she had removed}, guitar, and her bobbed haircut from her early days.
Her name could be a reference to Brian Eno, and her guitaring win pose shouts out to Eddie Van Halen.
And the solo she plays in that win pose sounds exactly like the beginning of the guitar solo in Mr. Crowley.
Faust, a.k.a Dr. Baldhead, is named for Johann Wolfgang Von Goethe's famous play, although he shares the name with the drummer of Emperor and the German band Faust. "Going My Way?" could possibly be referencing "Are You Gonna Go My Way?".
Leopaldon is the name of an electronica/house band.
Fanny, from the portable Guilty Gear Petit titles, shares her name with the alias of Fraser Runciman, a proponent of the breakcore genre.