The Beatles are widely regarded as the best musical act of all time; but when it comes to the most talented instrumentalists, we often overlook the fab four, on account of them not being technical and fast enough. In my opinion they were absolutely brilliant, each one of them had their own unique style of playing, each one of them had their own unique unorthodox approach to their instrument which made their tunes a beautiful amalgamation of four naturally gifted musicians contributing in a non standard style. 
That said it is true they did not know any theory and couldn't read music. Paul and Ringo were left handed and the other two were right handed.

Paul McCartney was probably the most musically gifted of the four, he could play the guitar, the bass, the drums, the keys and sing along each of them. Ringo only had a right handed kit when he started playing drums. He had to adapt his playing style to a right handed kit, and as a result the way he played sounded very distinctive and peculiar while still being in time. Tre cool of green day and Dave Grohl in an interview explained why Ringo's approach to drums was timeless and legendary.

John Lennon was probably the least technical of the 4, in an interview with the rolling stones he said that he couldn't jam around with his guitar like george and paul could, because he can't play that good. He was mostly a rhythm guitarist, but had a very unique style of songwriting on the guitar which was shaped by the fact that he learned to play a banjo first. 

George Harrison was the lead guitarist, personally I love how melodious and precise his solos and riffs were, they sounded brilliant, he gave the song what was required of it. In an interview he claimed that he would have been a much better guitarist had he not been in the Beatles. He also played the Sitar and introduced Indian music in the mainstream west.