I agree. “Greatest” is such an ambiguous word.
Even if you’re talking about raw talent, it’s hard to be narrow it down from there, and the determination is compounded by the progression of time.
For example: take Hendrix. At the time he was around, few others displayed such a command of the instrument, in terms of pushing the envelope, making good music, and sheer skill. Lots of people would swear by him. Today, though, the envelope has been pushed further, and peoples’ abilities have branched out, and the talent and virtuosity able to be displayed by guitarists has likewise increased exponentially. Tons of great guitarists rose to varying degrees of mainstream attention starting in the late 60’s, and the 70’s rock scene was overflowing with talented axe-wielders. However, in the 80’s, the electric guitar realm of virtuosity was again blown up wide even among the new wave generation, with such fantastic players as Eddie Van Halen, Randy Rhoads, and Kirk Hammett taking the electric guitar to then-unheardof places. Still today, from a technical perspective, there is no shortage of virtuosos, with guitarists like Yngwie Malmsteen, Joe Satriani, and Steve Vai continuing to amaze their fans with their mad skills.
Best style seems like more of a subjective thing, and by that I mean, relative to your individual tastes, which seems to conflict with the notion of greatest. I mean, someone might be the greatest to everyone else, but if you don’t like him or her, they obviously aren’t to you. Personally, I try to at least appreciate all forms and styles for what they are, so I don’t think I can provide even a decent answer to this question.
As far as most influential…like the skill thing, the factor of time plays into it. For example, as Suburban Plankton pointed out, Chuck Berry was incredibly influential, being one of the biggest influences, if not the single biggest, on rock and roll. Before him and after him, there were great influences both overall and in the various genres - Les Paul, Chet Atkins, Django Reinhardt, B.B. King, Muddy Waters, T-Bone Walker, a bunch of guys named Johnson…the list goes on. It’s really hard to narrow down the most influential…but I will offer one name - if I had to pick one for most influential, it’d be Les Paul.
Is it a coincidence that 2 of my guitars, the 2 I play most, are from the line named for and co-created by Les? Probably not. They’re incredible instruments. Besides being a very talented and incredibly influential guitarist, he was very instrumental (no pun intended) in the development of the electric guitar. 