This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
栧 is a rare character combining 木 (tree) with 曳 (drag, pull). The exact historical development is uncertain.
The left side is a tree 木, and the right side is 曳 (drag). Picture dragging a log or timber, but the exact meaning is unclear.
For エイ, imagine dragging a heavy log and shouting 'A!' (エイ) with effort: the sound エイ cues the reading while the tree component ties to the shape.