If you are sensitive to smells, covering them up may not work. Have you tried any of the air cleaners that are available? I know people who swear by them.
For cooking odors, install a better range hood that will really suck up the air. Also, if your kitchen has doors, close them when cooking to keep the smells confined. Or crack a kitchen window a few inches when cooking.
What kind of pet and what kind of pet odors? In general, brushing the pet (assuming it's a cat or dog), regular bathing of the dog (I'm not about to suggest regular bathing of a cat), frequent cleaning of the litter box, and regular laundering of pet bedding will help.
General stale mustiness--check to make sure no pipes are leaking anywhere that could cause mold. Do you live in a very humid climate? Then try a dehumidifier. But if you live in a cold climate and use central heating, you shouldn't be getting a musty smell that can't be eliminated with a few minutes of open windows and a cross breeze.
Fabric can hold odors for a long time. Consider getting furniture and carpets steam cleaned, and washing/dry cleaning curtains, comforters, throws, blankets--just about any large piece of fabric that you *can* clean, but don't clean very often. Also check your pillows and clean them if possible.