The second one is correct.Soil's= soil is.'soil' is the subject.'is' is the verb.'lateral'is the adjective.'displacements' is the noun.

well, I am no engineer, but I assume that soil is the thing that is experiencing displacement, and lateral indicates the plane of displacement? If so it should be 'lateral soil displacement(s)'. Not sure that the plural is required here, unless you are talking about multiple incidences of displacement. 'soil displacement' is the subject, and 'lateral' is additional information to describe the nature of the soil displacements. So soil and displacement always go together, and you can put 'lateral', or 'vertical', or any other descriptor in front. Hopefully that makes sense?

I would say that 1 and 3 are OK. 2 is a bit odd, as 'soil' is uncountable. By using the possessive, you are directly associating the displacement with a particular piece of soil, so it should be singular. 3 is better if you are stressing lateral (rather than vertical) displacements. 1 would be better if you are stressing the fact that it is a soil displacements rather than some other displacement.

These seem to be technical terms. You'd be better off asking this question on a forum that deals with agriculture.