Yes, it's safe to inhale essential oils through a diffuser or by boiling water in a large pot on the stove.
I run a diffuser all day long every day because I like the way it freshens the air naturally, but it's also great for a head cold.
Lavender smells wonderful, but it's not very potent against parasites. Tea tree oil, rosemary, eucalyptus and the other camphorous oils work better for me against pathogens. If you can find a good quality, pure Frankincense oil then that is supposed to be excellent for parasites, cancer, you name it. I have some from Aura Cacia and it's been adulterated so I don't recommend that brand for frankincense only (I use their other oils though). Cedarwood oil is also good for pathogens, but it's not as strong as the camphorous oils. I don't like peppermint--it gives me migraines, but you could try a very very small amount. Clove oil kills eggs, but it clogs up my diffuser, probably better to put that in a pot of water on stove or use topically.
Experiment with mixing them together. I like tea tree, rosemary and eucalyptus combined in equal amounts for sinus problems and to cleanse the air. Lavender and rosemary is a nice scent.
If you use a diffuser, one important tip is to never use citrus oils of any kind in it. The acid will corrode the plastics and it will shorten the lifespan of your diffuser.