Chemistry - How to properly store acids at home?

First I'd locate the bottle which causes the problem. Usually HCl is #1 suspect, but to be sure you can put a vial with smelling salts (aqueous solution of $\ce{(NH4)2CO3}$) or ammonia in the box with acids; white coating of $\ce{NH4Cl}$ on the bottle signifies the leak.

It's also a good practice to store acids in glass bottles with a proper joint (teflon ring) and a screw cap (e.g. Merck's SafetyCap). I would strongly recommend to get the proper bottles as soon as possible. Plastic bottles are only used to reduce the production and transportation costs, they are a poor choice for a long-term storing of chemicals. Even thick plastic is prone to diffusion, whereas glass is not; also plastic is, well, plastic, and is prone to mechanical deformations, so it's also tricky to maintain an impermeability of a bottleneck-cap joint over time.

In the meantime I'd wrap the necks of the bottles with parafilm, and/or pour some baking soda (sodium bicarbonate) on the bottom of the container where you store the bottles. This should help to neutralize the vapors before they reach the furniture and your nose, but it's a temporary solution.