The plastic part in the cover of my laptop is stripped off from the metal cover. The bottom grey part where screw houses are placed.
Which adhesive should be used to glue them back together?
First, I'd try to use a larger screw or to partially fill the stripped-out hole with something the screw could grip, such as a short length of solder or a toothpick. This allows later disassembly without destroying the case. Don't make the fit too tight or the plastic will crack around the hole.
If you do decide to cement the case together, use something that can be removed yet is strong enough to keep the shell together. Elastic glues or cements such hot-melt glue or fabric adhesive have enough flexibility and adhesiveness to hold without permanently bonding the parts.
I had this exact issue a few days ago.
While your mileage may vary depending on how much plastic you have left (since you said some of it came off), in my opinion, heat-setting is the best method. No adhesives are used and it tends to last longer and be stronger. However, there are compromises if you are limited on the depth or amount of plastic you have. Be prepared to possibly set the inserts lower than they were originally and understand you may need to use longer screws as a result (or just don't use the whole screw length--most laptops don't experience significant tension in all areas).
Here are two gifs showing heat-setting methods. I know the inserts in the gifs are much larger than laptop inserts, but the process is the same. A simple soldering iron does the trick. Don't apply too much pressure, let the heat do the work. Makes sure to use a pointed tip to make it easier to adjust and align the insert while it's setting, and a pointed tip is especially useful for the tiny inserts of laptops. A variable heat soldering iron is helpful if you have one.
- Soldering irons are hot. Be careful!
- Try not to sink the insert too deep or it will come out the other side and ruin the finish
- I suggest trying it out on the spare parts first to get the hang of this process--these things can heat up fast and it takes a bit of skill
- It can smell really nasty, make sure to have good ventilation and air flow
Hope that helps!