Use 'dislodge' when referring to removing obstacles or obstructions that are wedged or stuck. He used a stick to dislodge the leaves stuck in the drain.
Pro Tip 2/3
Difficulty Implied
'Dislodge' implies that some effort or difficulty is involved in the removal process. After struggling for an hour, they managed to dislodge the heavy rock.
Pro Tip 3/3
Not for People
Although 'dislodge' can be used for people in some contexts, it's more common with inanimate objects. The storm's winds were strong enough to dislodge roof tiles.