From the first pictures, specifically the one where it shows the rear axle bolt: it seems to stick out more than I remember (threads past the nut on the right side) on those bikes. That in itself isn't a big issue unless it points to something like this: once I got a bike in the shop (350 twin) that had the front wheel tilted on the axle. It looked really strange and handled worse. Turned out, the owner had replaced wheel bearings without installing the collar in between the bearings. After riding like this a while, one bearing loosened up a bit and tilted in toward the inside of the hub.The hint was that the owner had to "keep tightening the front axle because it was loose". He finally pushed the bearing inside the hub. The first clue I had was that the threads stuck out too far past the nut on the axle. The bearing finally fell inside the hub: I just got another collar and installed the new bearing: I could not get the old bearing out of the hub! It always rattled when riding slow...
My gut feeling from the pictures: one axle adjuster may not be set equal to the other. If someone swapped out one of the adjusters with one from another (possibly different model) bike, the hole for the axle could be too big, letting that side slide forward too much. (I'm thinking left side, here...). Or, the hole could just be centered in a different spot on the adjuster, so the marks line up, but not the axle. Since Honda shared many axles with different models, many of which used yet another chain adjuster from a different model, this can happen in junkyard swaps.
So, I'd measure from the swingarm bolt's center to the axle's center. Estimating from the picture, you have an "offset" of about 1/2" (13mm) of position (i.e., one-half the difference between the sides, where one is 1/4" and the other 1-1/14", if I understand correctly): this would only be 0.5"/9"=0.055" difference at the axle, side to side (in metric, about 1mm, not very much!). So, try measuring carefully from the axle center to the swingarm bolt center: that will tell the story, whatever it is. Then you can track down the cause.
Typically, the clearance to the brake arms on these bikes was about 1cm at the tire, if stock tires were used. The CB350F rear tire was only 3.75 x 18 when new, so if your tire is larger, expect less distance. I think the biggest rear tire that would fit the 350F was the 4.10x18 in TT100 V-profile, leaving about 1/8" clearance to the brake arm. I saw more than one brake arm modified for larger tires, some not too gracefully...
