Termites is a separate issue which has been discussed farther below. Try control and F and search on termites. That may be an expensive fix for your landlord to take care of. Dursban among other things is used to control those. Get a handheld sprayer to spray the foundation and areas where you have them. Look for dirt tunnels up the side of the foundation to find their entry point. Knock those off and spray. If you find tunnels then a heavy dursban barrier treatment in that area would be the first step but since they live in the ground and move around, you will need a barrier treatment all the way around. Watch for tunnels daily, knock them off one day and spray and their back the next. Be persistent.
For ants, buy a couple bags of dursban or diazinon and a hand held crank spreader. Put a fairly heavy band about 10' wide around the house. Repeat after rains. This banding will kill them in that area and keep them out of the house except if you have some carpenter ants living in the house. If your yard has lots of anthills, then treat the whole yard.
I had ants once and hired a pest control company. All they did was spray some on the inside and then sprayed a band around the foundation. Then came back each month to repeat. I learned to do it my self. I band every few weeks to keep out bugs, spiders, crickets, ants, etc. It is getting close to cricket season and it keeps them out. Occasionally I'll get liquid diazinon and a hose end sprayer (the type you can set the mixture on without any premixing are nice) to spray the band and then up the side of the house and foundation 2 or 3'. If I had a crawlspace, I would spray/spread some in there too. It will get those pesky spiders that reside under foundations. I'll cover all dog areas regularly to get rid of fleas and once a year in the yard for chiggers and any stray anthills.