It doesn't happen often. But when it does I know it. Despite my intentions my fathers words come out of my mouth. These aren't bad words or anything shameful. It is just that they are words that I had always associated with my dad and never expected that they would come out of me unknowingly. Jazz and Improvisation is like that too. Phrases, ideas, and gestures from our influences come out of our instrument. This happens in both intentional and unintentional ways.
My earliest jazz influence was The influence for improvised music post 1935. Charlie Parker. Next to Armstrong we can argue that Charlie Parker did more for the improvised solo than any other musician over the last century. Parker codified the way in which jazz musicians connect chord to chord while creating tension and release with specific chromatic alterations while maintaining both the sound of the blues and the beauty of a musical line. Whew! Sounds like a mouthful. But basically, Parker is the bridge from riff-based, swing-era solos and modern jazz.
As a young jazz musician, I began to play transcribed Parker solos from the Omni Book. At that point when you said "Omni Book" there was only one book you were referring to. But now, there are many Omni books, including Omni Books for Miles Davis, Cannonball Adderley, Wynton Marsalis, and many others. I played these solos until I could do them mindlessly, and invariably ideas would leak out into my improvisation. There wasn't much intention behind it, but I simply couldn't help Parker's influence coming out of my instrument. Now, I try to be intentional about what bits of language I am attempting to pick up. I might focus in on a lick, transpose into many keys, and work it into my solos through intentional practice.
Like many, I sometimes make the mistake of limiting the concept of jazz language to the specific licks that musicians play - but it is much more than that. We don't have to play an exact phrase to sound like our influential musicians. The way we play may carry even more weight. Phrasing, emphasis on certain parts of the phrase, the way we organize a solo are all part of a larger idea of language. I think even more than learning licks from the Charlie Parker Omni book, I learned his phrasing concept, which had a way of organizing my own solos in a very Charlie Parker-like fashion.
It is important to have influences. On a level we all know this, but are we active in our pursuit of learning from those individuals? Are we intentional about who they are and what we are trying to gain from them? Are we actively working to allow their sound to influence our own and come of out or instruments. Learning language is one of the best ways to connect us with the masters and anchor our craft in the history and tradition of this music.