Poke, prod, nudge, jog are comparable when they mean, as verbs, to thrust something into so as to stir up, urge on, or attract attention and, as nouns, the act or an instance of such thrusting.
Poke implies primarily the use of a body part (as a finger or foot) or of some instrument or implement (as a stick, a rod, or a poker), but sometimes, especially in verbal use and in idiomatic phrases, it may imply the operation of something equally effective in stirring up or in rooting out.
Prod suggests the use of something sharp which can stab or prick or goad into action; it may be a physical thing (as a sharp pointed stick) or it may be something less tangible but equally effective (as sharp words, a threat, or a taunt).
Nudge suggests gentler action than the preceding terms; it may imply the use of an elbow in attracting attention especially under conditions when speech is impossible or it may imply a mere suggestion or hint or it may imply repeated gentle action (as in moving or shifting).
Jog implies a thrust or, often, a touch on or as if on the elbow or arm that to some extent shakes one up.