Besides lavender, tea tree oil is also very well known for its antimicrobial, antiviral, antiseptic, anti-bacterial, anti-fungal properties and is typically used to treat a whole host of infections and helps to clear bronchial congestion..
From where I come from, eucalyptus oil is very widely used for its analgesic and cooling (warming oil) properties to relieve muscular aches and pains, fever, headaches, respiratory problems and can also be used to treat infections. It is very similar to tea tree oil and is inflammatory and acts as a deodorant.
Also, there’s rose hip seed oil. It isn’t really considered as an essential oil. Rose hip oil is very well known for its rejuvenating properties and is widely used to repair scars and skin damage from the sun (free radicals), age as well as from surgical and accidental wounds.