I read all the books and have no recollection of these 3 groups, but then again there is a lot from the books I have forgotten. From my memory of the books, GRRM really only takes one angle regarding Joffrey's murder, the angle that has been discussed already in this thread. Alas, I digress...
The below article is a really good read. It links to a lot of different fan theories and sites and then even quotes GRRM's Rolling Stone interview regarding Joffrey's murder.
NOTE, if you have not read the books DO NOT read the article.
http://flavorwire.com/451715/how-game-of-thrones-book-fans-investigated-joffreys-murder/
Littlefinger may have been part of the plot, or simply known about it. I am not, by the way, saying that Olenna and Margaery didn't kill Joffrey. The Tyrells are probably the strongest players after Littlefinger and Tywin, and Joffrey was dangerous to them. I am just saying I am not 100% sure. Even Martin's own comments point out that he has more to reveal about the events of the Purple Wedding.
I watched the episode again last night:
1) Olenna and Tywin are talking about how the Iron Bank always gets paid.
2) Cersei sends off the Pycelle, the one person that might have known how to save Joffrey, for a contrived reason.
I am going to let this sit for a while. For those just watching the show without reading the books, there are a few minor spoilers in this thread, but you will also note that even among the readers, and the author himself, there seems to be some ambiguity about this event.