salt, pickle, be dirty
腌 centers on preserving food with salt or brine: pickling. The 'be dirty' sense is a rare, possibly figurative extension of being soaked or stained, but the main idea is salt-curing.
腌 combines ⺼ (flesh, body part) with 奄, which likely provides the sound. The exact historical development is uncertain, but the character is associated with salting and preserving meat.
The left side ⺼ suggests meat or flesh, and the right side 奄 looks like a container with a lid. Picture meat being salted and sealed in a jar to pickle it.
For ヨウ, imagine yelling 'Yo!' as you toss salt into the pickling jar: Yo -> ヨウ, and the salt preserves the meat.