I had the same problem in my new house. Suspect that the insects came with our belongings from the old house.
Our solution (tried & tested and works!):
1. Buy those powder ant/cockroach poison. Crush some cornflakes and mix together with the powdered poison.
2. Take a sheet of paper (or newspaper). Fold it into a pop up triangle.
3. Use double sided tape on the inside of the pop up triangle. Scatter the poison/cornflakes mix on the doublesided tape.
4. Staple up the triangle so that it will not move out of shape.
5. Hide it in dark corners or near areas that you know have roaches.
6. Check every 2-3 days. You will find dead roaches very soon
1. Buy those lizard traps (using gum). I think I bought Combat (the brand).
2. Follow the instructions (remove the paper to expose the sticky gum, scatter some bait which is provided with the trap in the centre and leave in areas near where they are hiding).
For this, it can also trap the larger cockroaches. We use this in our car also.
Also, you can buy citronella or tea tree oil. Put a few drops in all your cabinets/wardrobe/behind mirrors. They do not like the smell, esp for citronella. It will also keep the mosquitoes away.