How is it called when someone is talking and cracking a smile at the same time, but in a way that only one side of the mouth is moved upward, like those villians in japanese mangas.
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"Sneer" fits that description:
A smirk is an “uneven, often crooked smile that is insolent, self-satisfied or scornful,” which fits the description perfectly. A sneer is a similar expression of contempt, but it specifically refers to a curling of the upper lip, not necessarily a smile.
A couple of related words are sneer (which as already mentioned has a meaning like “A facial expression where one slightly raises one corner of the upper lip, generally indicating scorn”) and sardonic (“Scornfully mocking or cynical” or “Disdainfully or ironically humorous” ).
In Google-image results for sneer and sardonic smile, the sneers are much more frequently like frowns than like smiles; and the sardonic smiles often are like sneers, and sometimes like frowns. Images for smirk seem to be mostly like smiles with a lifted corner.
Scoff, chaff, knock, jeer, gibe, flout, pan, and tease are all words I've seen in this context. Chaff and pan seem more friendly, flout sounds pouty or bubbly, pan and gibe sound more indifferent with knock being the most indifferent, jeer is where things start to become disdainful, and a scoff is downright rude.
Chaff - 'A joking, almost condescending smile.'
Flout - 'Express playful disdain for the rules: mock, scoff...'
Jeer - 'Cruel, insulting laughter, that shows disrespect.'
I've got to say, I strongly agree with the statement that a "sneer" is more like a snarl than a smile. Someone whose teeth are showing doesn't necessarily have his or her mouth turned upwards, and that's what a smile really is. I think that a "jeer" is the same as a sneer but with an almost definite smile.
Sneer - 'A grimace. Disdain, expressed by curling part of the upper lip upwards.'
Smirk is also great. It fits in somewhere between chaff and gibe.
Smirk - 'A fake, sarcastic, or invalidating smile.'