Some owls have ears placed with one higher, and the other lower. If an (otherwise normal) human were to have that sort of thing, only with their eyes sockets (and by extent, eyeballs). For the sake of the argument, let’s assume the right eye is about 3cm higher than its current position, and the left eye about 3cm lower. Would this have any beneficial abilities (like being able to judge height/distance better) or any adverse affects?
No beneficial effect
Assume there is a human that's got his neck crooked so that it's tilted sideways irreparably. Eventually his brain would accommodate to his eyes being at uneven height, producing a correctly aligned field of view, although it could potentially be flawed in diagonal direction (if the head is tilted to the right, then leftwards-downwards and rightwards-upwards areas will have weaker coverage, and vice versa), giving that specimen less chances of avoiding an attack from there. Yet, if your species would have uneven eyes placement, there should be an advantage first that would help eyes align in such manner, yet I fail to see any.
The detriments of having unevenly placed eyes could be numerous. For example, such placement would block or displace one side of that human's nose, the other side would have to displace the brain, also the "upper" eye would be less protected from falling debris, the human brows provide some shelter from small object and a capture means for tiny or smaller particles like dust, and the upper eye of your human would suffer from being open from zenith. Brain displacement might make one hemisphere less potent than the other, altering the core ways of how your humans think, having the lower eye too close to mouth cavity might result in occasional eye damage from eating hot or sharp stuff, that otherwise is blocked by a layer of bone we have, maybe more. I'd rather make your humans have three eyes, two normally aligned and one specialized on top between the nasal cavities and the brain, which would allow for tilted vision and normal together with better 3D senses.
You mention the misaligned ears without explaining why owls have misaligned ears.
First why do some owls have ears at different heights?
A: to change the arrival time of sounds.
With ears on either side of your head, it is very easy for a human to judge what direction a sound came from on the horizontal plane... However it is very difficult for humans to judge the distance to the sound and/or the height that the sound came from.
Try being blindfolded and have friends clap their hands at different angles.. YOu can tell exactly where what direction the sound came from.. Now try different heights at the same horizontal angle? You cannot tell anymore.
Now cock your head diagonally with respect to the source of sound. Suddenly you can tell what elevation the sound was produced at. We know where a sound came from by the distance in time it takes the sound to arrive at the right ear vs the left.
The cock eared ness of owls benefits them when they are hunting small rodents underneath snow.
So having cocked ears help owls determine where a rodent is underneath a snowbank because it changes the time to arival for of the souunds to each ear. Does the same thing work with eyes?
Maybe, but not in the same way...
Light is fast1 or so I have heard. The difference in time for light to travel to your left eye vs your right eye is so small it can be ignored2 your brain cannot judge the difference between the two. Which is your eyes do not use the delay between image arrival to determine anything...
So how do we have depth perception then?
We judge depth by the difference between what our right/left eyes see. The further apart your eyes are the better depth perception you can achieve because there will be a greater difference between each of the two images.
Putting your eyes diagonally, if it increased the distance between your eyes would therefore most likely increase your depth perception... However it is not because your eyes are diagonal.. but rather because they are further apart.
An example of an animal that benefits from widely spaced eyes is Hammerhead sharks who have incredible depth perception in a very small portion of their field of vision.
The downside with this of course is that the further apart your eyes are the less overlap there is between them so the area that your vision aligns becomes smaller and smaller. It is a trade off between better depth perception or a larger percentage of your vision gets depth perception.
1 like really, really fast.
2 It is less then the time it takes your photo receptors to realize that there was light.
Peripheral vision is kind of like 2 overlapping circles. Having them in the horizontal plane lets you see wider in this crucial orientation to spot lion, bear or rabbit, while there are fairly few interesting things above or below you need to spot fast (fruit won't run away and birds aren't really dangerous).
The effect of increasing distance between eyes, and especially by making eyes looking more "outward" you improve field of view at a cost of foveal vision. I guess, based on correlation with animals. Obviously, I am assuming human eye remains essentially unchanged, just moved and with the mandatory brain compensation that would happen.
So, this adaptation is pretty plausible only in special scenarios, especially where said humans aren't apex predators but prey of bigger beasts. For example, you would have one eye to guard against flying creatures (dragons, dinosaurs or whatnot), and the other against ground creatures like snakes. You would have worse sight overall ... but you would spot those nasties faster, so you would survive, unlike ordinary humans.
Diagonally placed eyes help you concentrate better. This is why humans grab their chins and tilt their heads while staring at that blank wall in the art museum.
They will also help you view things more skeptically. Unfortunate politicians with level eyes have to tilt their heads while their debate opponents are speaking.
If you would like to experience diagonal eyes, I recommend the excellent fashion choice of tying a bunch of bananas (7 or 8 should do) to your left ear. Once you are convinced of the advantages that this brings, you can have your left ear pierced and wear your banana bunch even more confidently. Just remember to swap out the bananas every few weeks.