Jimi Hendrix was left-handed and at the time he started to play the guitar, left-handed ones may have been hard to find, so he strung his guitar upside down.
Then, even he became rich enough to have access to any left-handed guitar he wanted, he kept playing on his reverted guitar. Was it just for personal visual style reasons or did it influence his playing, his sound on a way that he wanted to keep it?
The only thing I can see is with a reverted Strat, higher frets are harder to access.
There are many ways it would have affected his sound.
A few points about the interaction of pickups and strings changes.
The angle of the bridge pickup is backwards. This will cause his higher strings to be further away from the bridge where they pass over the pickup and his lower strings closer to the bridge where they pass over it. This will have caused his high strings to sound more mellow and his low strings to sound more sharp and biting.
On the headstock side, there is longer string travel on the bass strings and shorter string travel for the high strings between the nut and the tuners, as compared to a regularly Strat. The longer the strings travel the 'floppier' the string will sound. This one is more likely felt than heard but can definitely influence the player's technique.
The pole pieces which are staggered for certain strings sizes will be different and change the way individual strings sound.
A couple of points about the upside down body contour.
On a normally worn Strat the upper horn, which is the longer one, will have the strap attached to it. Wearing it upside down will bring the the fretboard further away from one's body. This will make fretting open chords and notes lower down on the fretboard harder to get to and notes higher up will be easier to get to.
The cutaways of the two horns are not equal. The lower horn on a regularly worn Strat has a deeper cut into the body to allow easier access to upper frets. Wearing it upside down will make access to upper frets harder and the player will have to adjust his fingering technique to reach them. This needing to work hard for upper frets is something many players of Gibson Les Pauls say influences their playing.
These two points sound contradictory and one might think they cancel each other out, but in reality it doesn't work like that.
I'll try to explain, however I'm no guitar maker or acoustic engineer so it might be quite technically inaccurate... Let's begin:
As you can see, there are 3 single-coil pickups on a Stratocaster. In this case, each pickup possesses 6 permanent magnetic pole-pieces that are located under each strings.
diagram of a single-coil pickup
When a string is vibrating, it creates variations of the magnetic field maintained between the coil and the string thus creating an electric signal sent via the guitar's jack (output).
Now, since every string has a different diameter, each permanent magnetic pole-piece is designed and ajusted (in height for example) specifically for each string. Yet, Hendrix was playing with a right-handed Strat and mounting his string in reverse order so he could play it left-hand. Consequently, each strings on Jimi's guitar were over the wrong permanent magnetic pole-piece, resulting in a slightly modified sound.
I think this is (one of) the reason(s) he kept playing on a reversed right-handed Stratocaster. However, there might be some other personnal reasons he had and that I'm unaware of.
