Soil, dirty, sully, tarnish, foul, befoul, smirch, besmirch, grime, begrime can all mean to make or become unclean.
Soil basically implies fundamental defilement or pollution (as of the mind or spirit) <why war soils and disarranges whatever it touches, I cannot say —Kenneth Roberts > <making that room our Chapter, our one mind where all that this world soiled should be refined —Masefield > but in much of its use it applies to a making or becoming superficially and literally unclean (as by spotting or staining or smudging).
In this sense the word is very close to the corresponding sense of dirty, which is slightly stronger in its implication of uncleanliness and especially of disagreeable uncleanliness; thus, “to soil one’s clothes” may merely imply that the freshness of a clean or new thing is lost, but “to dirty one’s clothes” usually implies some activity which has plainly left its unclean traces upon the garments. In its extended use, too, dirty tends to stress the unpleasant effect and typically suggests a making squalid or nasty of something that in itself is normal, wholesome, or clean.
Sully implies the staining or soiling of something that is pure, fresh, limpid, or innocent.
It is used more often in reference to immaterial or spiritual than to physical soiling.
Tarnish basically implies the dulling or dimming of the luster of a thing by chemical action (as of air, dust, or dirt).
In extended use it suggests a dimming rather than a total sullying of something of value.
Foul and the intensive form befoul stress a making filthy or nasty and apply either to a material or an immaterial thing. They often suggest pollution or defiling by something highly offensive or disagreeable.
Smirch and the intensive form besmirch may emphasize a discoloring by or as if by soot, smoke, or mud; usually they come close to sully in implying a destruction of immaculateness, but they seldom carry as clear an implication of an effect on real virtue or purity as they do of a darkening or blackening of appearance, reputation, honor, or good name.
Grime and the more usual begrime intensify the meaning of dirty and typically suggest deeply imbedded dirt often accumulated over a prolonged period.