Outdoor (WITHOUT s) is an adjective. Outdoor = located, suited for, or taking place in the open air: He enjoys the outdoor life.There are many outdoor activities in and around Coimbra.
Outdoors (WITH s) is an adverb. Outdoors = outside a building: He likes to work outdoors.
Outside = when you mean away from, use (get/go) out of (NOT outside): It does you good to get out of the city now and again.Without a passport, he would never have been able to get out of the country.
In British English, outside is not used with of: You aren’t allowed to park outside the bank.
In American English, both outside and outside of are used.