Just how this word communicates its sense is likely to rely to some extent on the accent of the speaker. The rounder vowels of Received Pronunciation give a starchier, rigid, turned-up-nose approach, like the objection to the object; the flat, farther-front sounds of a Northeastern US accent (say, Buffalo) practically epitomize the offensive object itself, like a motor scooter by your bedroom window at 3 AM or a nose full of vinegar.
Speaking of noses, doesn’t that bnox seem like a box on the nose (or, worse, a stop in the Bronx)? And o, o, o, look at the visual rhythm of the word: three o‘s, each followed by two other letters; and the heart – with four letters before and four after – is that x, sign of proscription and, in cartoons, of queasiness or unconsciousness. This word is tightly constructed, but just to annoy you.
Like so many of our most expensive words (including many of those with x), this word comes from Latin: ob “towards, in front of, etc.” plus noxius “harmful” equals obnoxious “exposed to harm, liable to punishment.” Oh, wait, what? Yeah, originally to be obnoxious was to be exposed to harm. The sense shifted, though, and didn’t take all that long to do so, probably under the influence of the noxious part, and I’m sure the obstinate ob of obstacle, objection, and other things that get in your way played into that.
And what is most often obnoxious these days? Behaviour. And things that are obnoxious are often rude and/or loud. But, interestingly, they are often not actually harmful – just annoying. But deliberately so!