To burn alot of calories in an exercise, your looking at trying to get your heart rate as high as you possibly can. You are unlikely to be able to do this in a small space unless you buy a treadmill (which infact is not so small and may not fit). The best types of exercise you can do are ones which have you move around as much as possible. Running, skipping, rowing (with real water- those gym rowers are nothing compared to real rowing!), cycling... you are unlikely to be able to do these indoors, even if you did have alot of room.
I see no problem in going outside to run or cycle to work and back every day. This will do more for you anyway then gym machines in my opinion as gym machines tend to work you in a very mechanical way where as outside running/cycling/whatever you chose tends to work with more of a 3 dimensional type of working.
I would say though that doing cardio (cardio burns calories) outside in the middle of the night would not be in your best interest. Its likely to give you an adrenelin boost which may mean your going to find it hard to sleep or to sleep properly. Try if you can to work out when the sun is still shining, it will help you to maintain a decent sleeping pattern. Sleep is important as a lack of it will mean its hard to maintain any sort of diet plan (if you want to lose weight, what you eat matters more then exercise although exercise is important). The last thing you need is to ruin all your effots because its too hard to stick to normal portion sizes!
If you are set on doing some work inside, (though this wont burn many calories it will help you build or maintain muscle which will help you with your cardio- you can do more with more muscle) you could buy a few sets of dumbells, as long as your not stupid with them, you wont be throwing them around and there are multiple exercises you can do with them. Many are listed on the site.
If you can, get a heart rate monitor, Garmain if your wealthy, Polar if your not (there are others but these seem to get the most votes). Ignore any calories they say you burn, they are often wrong on any machine and look for the heart rate. Your aim is to keep your heart rate up when you exercise as this is what means your body is burning more calories.
And finally stretching- this can be done at home