Nah, neither are triggered by the Vagus, but the Vagus has a role in both of them.
The nervous pathway for sneezing is:
Sensory (afferent) stimulus from the nasal cavity is carried along the nasociliary branch of the Ophthalmic (V1) division of the Trigeminal cranial nerve (CN V). The motor (efferent) impulse is carried by a number of different cranial nerves:
a. Vagus (CN X - causes contraction of the diaphragm muscle, as well as muscles of the larynx & pharynx)
b. The medial pterygoid branch of the Mandibular division of the Trigeminal cranial nerve (causes contraction of the tensor tympani & tensor veli palatini muscles)
-contraction of tensor tympani basically keeps the force of the sneeze from messing with the sensitive parts of the inner ear
-contraction of tensor veli palatini helps mitigate the force transmitted to the nasal cavity from entering the eustachian tube)
c. The branchial motor component of the Facial cranial nerve (CN VII - causes contraction of multiple muscles)
-contraction of stapedius helps to keep the stapes (one of the inner ear bones) from getting messed up
-contraction of stylohyoid & digastric helps stabilize the throat & neck
-contraction of orbicularis oculi makes your eyes close (so they don't pop out of your head!)
-contraction of various other facial muscles produces the wince
d. The Glossopharyngeal cranial nerve (CN IX) is probably also involved since its branchial motor branch innervates stylopharyngeus (contraction of which helps stabilize the neck and throat)
e. Various upper thoracic nerves are probably also involved since they make the muscles of the upper chest & back contract.
Orgasm is much more complicated in its neuronal pathways, since the pathway & muscles involved in penile & clitoral erection are different from the pathway & muscles involved in male ejaculation; the pathway for orgasm itself is also different. You can find these on the web, just google "nervous pathway orgasm" or "nervous pathway ejaculation", etc. Sorry for kinda ducking this part of your question but I know a lot more about cranial nerves than other nerves.
As for the involvement of the Vagus nerve in orgasm, mammals are unique in that our Vagus allows us to disengage our cardiac output (read: heart rate) from the external environment & modulate it according to the social environment (in other words, doing things in a social setting, or in this case, doing people, can cause our heart rates to rise or fall, which is necessary for knocking boots).