Here are a couple of tips!
1. Come up with 2-3 generic poses that match the character's personality. Q is a smart guy, a puzzle solver, so poses where you look like you're deep in thought will work well. Loki is a trouble maker who wants control-- mischievous smiles, dramatic hand motions, and wide/open poses where you're trying to look larger/more intimidating than your photographer will help that come out in photos.
General posing tips!
1. Do a 3/4s turn. It's generally a very flattering angle that also shows off more details of your cosplay! Standing sideways makes your size very noticeable, and straight head-on shots tend to make you look 'flatter' (and generally not as dynamic) in photos.
2. S curve
. You don't need to put your arms up like the models in these examples, and it generally is better for female characters, but shifting your weight to one foot can help make a difference and make you more interestingly posed. (Think about the 'line of action' in comic book art-- that applies to photos too!)
3. Chin out. Helps prevent the 'flatness' that the camera always makes. It's also more confident!
4. Research! Go back to the media you're cosplaying from, and pay particular attention to your character's body language. Look for cosplayers who have done the character you want to cosplay before, and see what you like about their photos (if anything). If it's a good photo, check out the pose, and try to do something similar. If you feel the photo isn't so great, figure out why and don't
4.5-- Research stuff that's NOT your cosplay! Just poke around the cosplay tag on DA, Tumblr, or galleries here. Maybe somebody else has done a set of two characters with similar personalities and have great poses already figured out.
5. Ask your photographer! A good photographer will at least have a couple stock poses to put you in, and if they're super awesome they'll have character-specific ideas.
6. Use your surroundings! Sit on things. Lean on things. Interact with what's around you. You're probably shooting in a particular location because it's character-suited; what would they do if they were there?
As for partner posing...
1. Levels. Just having shots of you both standing side by side for an entire shoot is boring.
Try ones where one is standing, one is crouching; one standing, one sitting; one lying down (dead maybe?), one crouching.
2. Interact! You're cosplaying that particular duo for a reason. What's their dynamic? Figure out what you/your cosplay partner is comfortable doing, and play off of each other.
3. Talk to each other! Maybe your friend has ideas too. Maybe you're posed in a way that is physically difficult (standing on tip-toe, holding a crouch for a very long time, balancing on something a little unstable), and having a "spotter" helping you is awesome. Maybe you're just joking around in-character and get a great idea as a result!
Elite Cosplay has a bunch of awesome posing tutorials on YouTube that might help-- this is the intro one