So...I adopted a few pets that have jobs and bring be home some bank. Which is awesome, but the job agency only wants pets with high level, strength and intel. I already know how to raise their intelligence, but how do I level them and make them stronger?

Train them here. http://subeta.net/explore/train.php

You have to increase Level first and then you can increase the other stats.

There are TONS of ways to train your pets, easiest IMO is the Training center

But there are also items click here to see to increase stats (though expensive esp when first starting out) and you can do battle quests which give you exp and you can spend them on points under the battledome tab in games

yeah training center and you can train them every 51 mins