I feel strange.

Literal

Strange feeling [subject-が] does.

変な感じがする is a useful template: [adjective] + 感じがする = 'I feel [adjective]' / 'it feels [adjective].' The が marks 感じ as the subject of する. This pattern works for physical sensations (痛い感じ) and abstract feelings (嫌な感じ) alike.