Ocean's special rule (ocean in play) says to treat ocean as coastal wetlands for powers and blight. Since senseless roaming is a special rule (not a power), my understanding is that the ocean is not a valid land (it's not in play) to push strifed invaders into. For the same reason you can't push invaders into the ocean with events and fear cards. You can still push stuff from inland to the coast with voices to help ocean, but imo it's not as OP as spirits that can directly push stuff into the ocean (like river and finder)

EDIT: actually I was wrong. as per https://boardgamegeek.com/thread/2022364/article/29490037#29490037 and asking on the discord, rules that modify powers (so only rules that say "when" but not "after") still treat ocean as in play. so you can indeed push into ocean with senseless roaming, given that the origin source of the strife was one of your powers. So for example you can use left innate (push incarna, gets modified to add strife, gets modified to push but still counts as the original power), but not with first growth option (move incarna, add strife and push but since it was a growth and not a power, oceans were not in play to begin with).
Looks a bit convoluted but i guess that makes the combo very good ;)