cane, walking stick
枴 centers on a wooden support used for walking: a cane or walking stick.
枴 combines 木 (tree/wood) with 叧, which likely contributes the sound. The exact origin of 叧 is uncertain, but the character is used for a wooden cane.
The left side is 木 (wood), and the right side 叧 looks like a bent stick with a mouth-like opening. Picture a wooden cane with a curved handle that you grip while walking.
For カイ, imagine a cane that makes a loud 'kai!' sound when it hits the ground: kai -> カイ, and the wooden cane taps the floor.