Intransitive verbs and verbs without e, do they have an oblique more often than not? In otherwords, do they act like the English "to speak of something," or the various IE languages that don't characteristically take the accusative, but instead take a genitive, dative or the corresponding prepositional phrase. My search probably discarded a lot of valid verbs that use obliques, but I think the pattern remains. There are probably a lot of verbs that take both an accusative and an oblique (mi pana e moku tawa jan), but that would be a harder set of searches.
kepeken, lon tawa are common obliques for many verbs. weka seems to have an affinity for tan.
The most common oblique constructions are:
li toki kepeken
li toki tawa
li pana tawa
li weka tan
li lukin tawa
sama doesn't really seem to fit the whole pattern. No verb has a strong affinity for poka, lon insa/anpa/sewi/sike. Lots of verbs occur with lon, but there doesn't seem to be any particular affinity between them.