Is there any way to make a good case without an oven or machine to cut plastic? Could I use wood that I carved or would the laptop/xbox 360 overheat? Could I use hot water or a lighter to shape the plastic or would that give out toxic fumes that kill me ? I live in a country where apartments don't have ovens and I am limited to what I can fit in my place since it is only 20m squared in size.

I'm no expert (not even close) but I don't like the
chances of the wood NOT catching on fire.

Try purchasing plastic already cut to shape and assemble it with plastic cement or glue?

You can use Plexiglas and PVC cement as aforementioned.
I also favor using the plastic cornering for drywall that is $4 per 6 feet or so.
I makes for a cleaner look, and adds some strength.

I made a deskbook with that design.
viewtopic.php?f=17&t=43812

The only way to make good case without an oven or machine to cut plastic is what Reaper mentioned.You should try using Plexiglas and PVC cement as aforementioned.Hope it may help you to make good case.

there are a lot more ways to make a good case without those resources.

Just off the top if my head, here are a few:

they made the statue of liberty by making wood forms and hammering copper around the forms with an assortment of forming hammers (ball peen and such), that would be a great way of making a case which can either be painted, lacquered, or left to petina and look a bit like a steampunk device. For forming the wood, all you would have to have is a block of wood, a wood file (rasp), a small hand saw for early shaping, and sandpaper to get it down to what you want it to look like.

You could plaster-form a mould for pouring epoxy resin into and making a cast case whatever coloring agent you mix into the epoxy. plaster forming is pretty easy especially for something that just needs to hold epoxy in place as it dries, same thing to finish the plaster mould as the wood, a rasp and sandpaper, though a can of computer dusting canned air would help a lot. do the sanding outside sitting on a sidewalk or something so you dont make your room a plaster dust covered mess. The epoxy would need sanded and polished after being cast, but again hand tools can do that.

You could also search electronics project distributors for project enclosures that come close to what you want, and though I am not sure they ship internationally, www.polycase.com would be a great place to look at and see what is available premade for you.

All of these would of course be much easier with a couple power tools, namely a good dremel and bit set for it along with a vibrational sander and finish sander, but everything could be done by hand with some effort.

you should really look at
www.polycase.com
go ahead and purchase a pre made case.
wood would (no pun intended) not be a good option for a case.