Drywall before or after vent installed

I would probably use some rigid foam insulation (2 or 3" is probably good, it's generally rated at R7 per inch - and you can stack it, it doesn't have to be a solid piece), and then use spray foam to seal it up around the edges and hold it in place.

It looks like a metal sill all the way around, so that's going to cause a lot of heat transfer anyways - ideally, to make it as warm as possible, get rid of the metal. You can also then pull off the trim and just put some backing in, and a piece of drywall (or plaster) to finish up the inside.

The most important part is making sure it's sealed to the elements from the outside, like rain/snow. You don't want water coming in and getting into your walls. Depending on the outside condition, get rid of the louvres. Ideally you would put a piece of plywood in place and then if you have siding on the rest of your house, put siding over that as well. You might also be able to just leave the lovres there, but seal them up (with caulking outside, spray foam inside) so they don't open and don't let anything in.

You need vapour barrier (the plastic you put up before drywall) and air barrier.

To count as an air barrier you stop air flow by using sheathing tape on:

• OSB joints and edges
• Vapour Barrier (this is most common)
• Tyvek Housewrap seams (becoming more common)

Some people think that you only need a vapour barrier or that the vapour barrier is also an air barrier. This is not true. You can make it an air barrier by sealing the joints and seams with tape and mastic, but otherwise it is only to stop Vapour Diffusion and not Air Flow.

Long story short: you had condensation because you did not have a proper vapour barrier, air barrier, or both. Since you seem to have a VB built in to your insulation, all you need to do is tape the seams and seal the edges at the top and bottom plate to make an air barrier.