I am tryiing to find a device that I can use to prevent someone from opening it from the outside. I can't install deadbolts on these two doors and I myself have been able to gain access to the house in 4 seconds with a credit card once when I was locked out. I want to prevent someone else from doing the same thing. I don't want to spend a ton on them since I need two.

One idea that I did to our doors since I also rent and our doors just didn't lock well was added chain locks. They are cheap and I think very safe.  Now this will be good as long asyou are in the house but it won't work when you leave.   I don't think there is any kind of lock you could put on outside for when you are gone unless you contact your landlord ot install new locks.
Good luck with getting your doors fixed.  Thanks for using IMshopping!

A great idea is the Secure Port Door Lock SPDL-1. It is a portable door lock that requires no tools to install. It fits most standard doors and can be taken with you when you move or even when you are on vacation.

I know you said you wanted a device but have you tried fixing the door hinge itself? By what you are describing it seems loose. To fix this, first try to simply tighten the top hinge. Tighten it tight but don't do anything that will risk stripping the screw in hole. This will only loosen the door more. I suggest when you do this, only tighten the top hinge. Leave the others alone. By tightening the top hinge only, the door will stand up straight again.

• If this doesn't work, it is because the screw is not 'biting' into the wood as well as it used to. To remedy, buy a longer screw (you may be able to get away with just one) and replace the top screw in the top hinge.

• But if you dont want to try and fix it manually I came across the perfect door jammer to help you out! This will prevent anyone from getting into your house,especially in 4 seconds! Its called the TAC Wedge and its a powerful tool that can keep your door shut or openned.

For your needs I'd seriously consider the Lock Rail security system.  I've listed other keyless security options that may be in your price range.  Good luck!

Anchored securely to the floor, this beautiful Home Security Door Lock adds maximum security to your entry doors.
Simply slide the Lock Rail into the floor plate to lock the door. Remove it and the door swings freely above the floor plate.
You can feel safe in your own home.
Try the new NIGHTLOCKTM