rat, mouse, dark gray
鼠 centers on small rodents: rats and mice. The color sense 'dark gray' is an extension of the typical grayish fur of these animals.
鼠 is a pictograph of a rat or mouse, with the modern form preserving a stylized head, body, and tail. The exact historical development is uncertain, but the character has long represented rodents.
The top part looks like a rodent's head with whiskers, the middle box its body, and the lower strokes its tail. Together, 鼠 is a rat or mouse.
For ソ, imagine a small mouse sewing a tiny gray coat: sew -> ソ, and the mouse's gray fur matches the thread.
mouse; rat
squirrel (any mammal of family Sciuridae)
hedgehog (any mammal of family Erinaceidae)
sea cucumber (Holothuroidea spp.)
brown rat (Rattus norvegicus); common rat; street rat; sewer rat; Norway rat
groin; inguinal region
rat poison; rodenticide
Japanese dormouse (Glirulus japonicus)
squirrel monkey (esp. the common squirrel monkey, Saimiri sciureus)
cornered rat
guinea pig (any of five guinea pig species, esp. Cavia porcellus)
naked mole rat (Heterocephalus glaber)
shiny guinea pig (Cavia fulgida)
southern flying squirrel (Glaucomys volans)
kangaroo rat (of North America; any rodent of genus Dipodomys)
common squirrel monkey (Saimiri sciureus)
Siberian chipmunk (Tamias sibiricus)
Laxmann's shrew (Sorex caecutiens); Baikal shrew
Brazilian guinea pig (Cavia aperea)
montane guinea pig (Cavia tschudii)