lie down, recline
躺 centers on lying down or reclining, typically with the body stretched out horizontally.
躺 combines 身 (body) with 尚, which likely contributes the sound. The character is a relatively late formation for lying down, with the body radical indicating the physical posture.
The left side 身 is a body, and the right side 尚 looks like a person stretching out on a mat. Picture a body reclining comfortably.
For トウ, imagine lying down on a soft towel: towel -> トウ, and your body stretches out on it.