Steve:
Since Steve took the super soldier serum he can't get drunk, and you don't drink too often particularly with him. Sometimes though you need to relax and let loose a bit. Steve doesn't judge and he thinks you're cute when you're drunk because you are a clingy drunk. Steve doesn't have to worry about you running off to go dance with random guys at a party, because you are basically glued to his side.
Bucky:
You become quite the partier when you're drunk and become a lover of karaoke which you can even occasionally convince Bucky to join you in, if he's drunk enough. This of course takes quite a bit more alcohol than it would for most, but he eventually gets there and it's hilarious. After partying and singing together, you two will head home and when you're cuddling before you fall asleep you whisper drunken, and incredibly affectionate comments to one another.
Pietro:
Due to Pietro's speed he metabolizes alcohol too fast too get drunk, but he will still drink with you any time you feel like it. When you get drunk you suddenly become a comedian, constantly cracking the greatest jokes, well at least that's how you see it at the time. In reality the jokes you make are probably the worst in the world, but they are so bad that Pietro thinks they're hilarious and loves them.
Loki:
You both have a tendency to get incredibly philosophical when you're drunk and enjoy talking about the future as well. After you both have a lot of drinks you usually find yourselves lying on your backs on the carpet next to each other. You both stare at the ceiling talking about the universe and hold your hands above your head to "illustrate" your points, then you spend hours talking about your future together.
Clint:
You are a pretty relaxed drunk while Clint is an incredibly hyperactive drunk. When he starts to get buzzed he'll also starting drumming his fingers on EVERYTHING, including you. By the time you're both completely drunk, you will generally find yourself sitting back and watching while Clint "dances" around the room. That term is used quite lightly though because what he does is less dancing and more like wild limb flailing.
Thor:
Thor is a very loud and excited drunk who likes to tell stories of Asgard. When he tells these stories he will practically be yelling every word but you don't mind. You are quite the happy drunk and love hearing his stories, even the ones you've heard a million times before. You will be laughing the entire time and eventually you try to make food for the two of you and fail, which will definitely entertain Thor.
Tony:
Tony is a horny drunk, luckily for him you're not that innocent yourself when you get drunk. When you two are with other people you'll try to hide the drunken lust you're both feeling, but that doesn't always last. When Tony is no longer able to hold himself back he will bury his face in your neck and start to kiss you, this will drive you crazy and then it's you who can no longer hold out. You'll quickly excuse yourselves and run for the bedroom.
Natasha:
The two of you are super giggly and cuddly when you're drunk together. Usually the two of you will be watching James Bond movies in your apartment when you get drunk together and you will both be laughing non-stop by the end of the first. You two shares drinks while cuddling on the couch and also trying not to spill the drinks on the couch, which is quite hard when you're laughing that much.
Wanda:
Wanda is an adorable drunk and becomes completely obsessed with random objects, like a pencil or a snow-globe. She will pick up these objects and stare at them for what seems like forever and you will be staring at her the entire time. When you get drunk you become hyper focused on her, and a little paranoid that somethings going to happen to her. There's no particular reason for it, but some people are paranoid drunks and that includes you.