rinse, wash, gargle
嗽 centers on cleansing the mouth and throat with liquid: rinsing, washing, or gargling to remove impurities.
嗽 combines 口 (mouth) with 欶, which likely contributes the sound and is associated with sucking or drawing in. The character expresses rinsing or gargling actions involving the mouth.
The left side 口 is the mouth, and the right side 欶 looks like a person 欠 using a wooden 木 tool to draw liquid. Picture someone rinsing their mouth with a wooden cup, gargling to wash it clean.
For ソウ, imagine a person gargling so vigorously that they make a loud 'sow' sound, like a pig: sow -> ソウ, and the mouth 口 is busy rinsing.