From Old Norse 'oddi' (point, triangle) — the unpaired point of a triangle became the concept of 'unpaired,' then 'strange.'
Strange or unexpected; not divisible by two without a remainder.
From Old Norse 'oddi' meaning 'point of land, triangle, odd number,' from 'oddr' (point of a weapon). A triangle has an odd point — the third angle sticking out. That unpaired point became 'odd' (unpaired, then strange). Key roots: oddr (Old Norse: "point, tip").