Locutionary and illocutionary verbs are not a thing, as far as I know. Locutionary and illocutionary acts on the other hand are well known to me and to others as well. I think an example will help you here.
In my Semantics course a third speech act facet was presented as well, though. It is called perlocution and refers to the effect of an utterance on the listener, i.e. whether or not the utterance leads to the desired result by the speaker. This needs not necessarily be applicable to all cases, so that is possibly why you have not heard of them or read much about them.
Ex.: "I am cold."
Locutionary act: the grammatical properties of the utterance and the declarative nature of it.
Illocutionary act: The actual nature of the utterance that is meant by the speaker, i.e. a request if the hearer is able to do something about the speaker being cold. Depending on the context, this can be a request to close the window or to start a fire in the hearth (or perhaps a little less ancient: the central heating).
Perlocutionary act: The effect the utterance has on the hearer, i.e. (not) closing the window or (not) providing a heat source.
Another quote to strengthen your understanding is as follows. From "Semantics" (3rd ed.) by John Saeed. Chapter 8, paragraph 2, subparagraph 5:
Austin proposed that communicating a speech act consists of three elements: the speaker says something, the speaker signals an associated speech act, and the speech act causes an effect on her listeners or the participants. The first element he called the locutionary act, by which he meant the act of saying something that makes sense in a language, i.e. follows the rules of pronunciation and grammar. The second, the action intended by the speaker, he termed the illocutionary act. This is what Austin and his successors have mainly been concerned with: the uses to which language can be put in society. In fact the term speech acts is often used with just this meaning of illocutionary acts. The third element, called the perlocutionary act, is concerned with what follows an utterance: the effect or ‘take-up’ of an illocutionary act. Austin gave the example of sentences like "Shoot her!". In appropriate circumstances this can have the illocutionary force of ordering, urging or advising the addressee to shoot her, but the perlocutionary force of persuading, forcing, frightening, etc. the addressee into shooting her. Perlocutionary effects are less conventionally tied to linguistic forms and so have been of less interest to linguists. We know for example that people can recognize orders without obeying them.