How to handle lingering smells?

You’d have to identify the source of the smell, but activated carbon/charcoal is the best thing I know of for absorbing smells.

Try leave the windows open for a while if you can. Sometimes you need to air the rooms.

Thank you @Kropotkin and @NerdyKeith :D

If smells give you a headache then spraying air freshener can’t be helping much. As you say it masks the smell so now you have two smells to cope with – double trouble! Good advice above – you could also try vacuuming your soft furnishings and damp dusting to pick up residue that smells

Buy a negative ion generator. Those things work wonderfully at cleaning the air.

Replace your carpet with hardwood or tile flooring. Replace your cloth couch with a leather or leather-look one, and wash your curtains regularly.

Textiles hold in scent particles.