The first 2 work best. The rest of them sound kind of awkward to native speakers.

Adding emojis can also make it seem more informal and friendly if you’re texting, but in conversation just asking “do you want to go to the movies tonight?” is also good.

The first one ("Would you be up for...") is the most common among all ages, at least in the United States. You could also ask more simply: "Are you up for a movie tonight?" The idiom "to be down for" is still used, but it is a bit dated. It was more popular about 15 years ago. So people who say it now were probably teenagers in 2000. However, you will still hear younger people saying "I'm down" by itself to mean "yes" in reply to a question: Person A: "Hey, a bunch of us are gonna walk the old train tracks tonight. You wanna come." Person B: "Sure, I'm down." Notice the informal language throughout: "Hey" ... "bunch of" ... "gonna" ... "wanna" ... "I'm down." That is to show that this is very casual conversation. You'll see such language in even shorter format in texts: Person A: "Train tracks tonight?" Person B: "I'm down." The third and fourth versions of your posted question, while the grammar is OK, are not natural speech for English speakers (though even then, I would expect to see "accept going" in place of "accept to go").

How about movies tonight?