[RPG] Can a multiclass character worship different deities

Pretty much all rules dictating deity worship are gone in 4e, replaced with DM discretion and recommended threats of story-based consequences for unpopular actions or beliefs within a subculture.

Additionally, there is nothing in the rules preventing a character from worshipping multiple deities, cherry picking which parts of each that appeal to them. The PHB openly states, “Most people revere more than one deity” (PHB pg 20), but most people are under the impression that, because the online tools only allow you to select a single Deity, that players can only worship one. This is point-blank untrue, and furthermore, wouldn't make much sense within a provably polytheistic society.

So your character could worship Sune because she embodies the ideals of Beauty and Trickery, and another evil deity of your choosing that embodies torment and madness. The two would combine nicely in your concept.

Another twist I've used before successfully is a character who believes that she worships one deity, but who is in fact interacting with another entity entirely.

Perhaps the most well-known iteration of this kind of story arc is Pelor the Burning Hate, but it doesn't have to be a universe-wide deception by the deity, it could just as easily be a case of an individual or single temple being fooled by a fraudulent impersonation of their intended deity.

In this case, such a character could honestly believe that they are worshipping Sune, but their prayers are being intercepted and answered by Cyric, the Prince of Lies, who is attempting to gain enough influence to break free of the prison that Sune helped build for him.

His alignment could have aided in the slow corruption of your PC, and the illusions afforded him by the trickery domain would be neatly augmented by the madness and strife slowly creeping into your PC's demeanor.

It's up to your DM how to adjudicate things such as feats, paragon paths, or epic destinies which require one to worship Sune, but thankfully there's only one of each, and none of them are stellar picks.

It is possible for celestials, even the most powerful ones, to be tricked by evil deities. They might become pawns, initially unaware that they are being played with. They might eventually get corrupted and fall. A famous example is Malkizid, a solar who was seduced into betraying Corellon by Lolth, and was later cast into the Nine Hells. Another example (from 3.5e) of a celestial actively serving an evil power was Thah Rhalar, a hound archon minion of Set.

If you want some inspiration about how to modify celestials to serve evil deities, you might have a look at the description of angels serving the God-Pharaoh, who is actually the malevolent dragon Planeswalker Nicol Bolas, in the Plane Shift: Amonkhet write-up available as a free pdf from WotC. While not legal in Organized Play events, it is still some kind of "official" D&D-5e-compatible material.