Tramp (usually used as a verb) = to walk in a resigned manner..., not enjoyable. ie to tramp around busy stores.
Trek = usually a long, tiring journey, originally used to describe a migration of people from one part of the African Cape region to another area free of government. Not undertaken for pleasure
Excursion = A short duration trip taken for pleasure. Usually begins in a vehicle followed by a walk around a place of interest and return by vehicle.
Expedition = A journey undertaken by explorers or scientists or adventurers to fulfill a scientific aim or physical challenge.. This requires a great deal of planning and preparation.
Hike = a long walk undertaken for pleasure, usually strenuous, in wilderness areas.