Well this many posts in just one week after you started this
thread! For what solace it is, at least you know that we feel your pain. However nice it would be to convert your neighbor, it looks like little chance for that. But I have to give a nod to Matt Johnson for his idea which incorporates at least a step in that direction and also put a good foot forward should you be lucky enough to have those bad neighbors move because it would reflect better on you if new people moved in and were greeted with something much nicer than a quasi spite fence.
We who are responding here might be able to give better or maybe even "inspired" responses if we could see a plat of your lot. Perhaps you could go to Google Maps, find your address, put the map in satellite mode and do a maximum zoom. Then do a screen shot and post it here. Be sure to include the usual map scale line so that we can get the measurement, although if the property boundaries of your lot are clear we can use those with the lot size info you have provided. We could then better see your predicament and you would not have to give your address away. If the above imaging steps are beyond your current computer skills I am sure that there are many here that could help with that step..
For what you desire to accomplish I doubt that just a fence of any sort all by itself will be satisfactory. But a fence of a wire mesh sort plus a tall hedge should do nicely though you may lose the spring sunshine in part of your back yard.
I put in a chain link fence to keep the neighbor kids from using our lot as a shortcut. There are chain link posts that are driven into the ground and then an angle plate slips over the top and is driven into the ground with a 4 pound short handled "Blacksmith's hammer". This sort of fence, goes in quickly without
concrete and is more easily repaired if someone backs a car into it. That however would be a first step and animal deterrent. However Given that these neighbors appear to be the disagreeable sort, make sure that the fence is located legally. If there are survey stakes placed on the lot make sure that no one has moved them. If at all possible get the neighbor's agreement that where you are putting the fence is not violating their boundaries. And consider that you may not be the only one wanting a fence, if the other neighbors want a fence too, you might get a better price from a fencing contractor if you are using the services of one.
The next step would be to plant a hedge of sorts. I am a strong advocate of bamboo. In your colder climate I would be inclined to go with a "clumping bamboo" It does not spread like a running bamboo and in a few years you could have a 20 foot wall of green graceful bamboo waving in the breeze. You should be able to have a bamboo that holds its leaves all winter and since the neighbor is to the south any drifting snow from a snow fence effect should dress up his yard in a clean white mantel. Although the clumping varieties tend to grow slower and you will have to plant quite a few because they do not grow as fast as the running variety, still they are fairly fast growers. Foliage as a barrier also dampens sound and filters odors such as tobacco smoke etc. and growth height is less likely to be regulated by the town.
Although it is likely to be slower growing various evergreens may be a good consideration and you should visit your
local nurseries to see what varieties they might recommend. You can be pretty sure that they have dealt with this sort of problem before and they may be able to do the heavy work on this if you need them to.
Do you need or can you use and will the city code allow you. a storage shed in your back yard? I.E. a place to park the lawn mower and garden tools. that might be a useful investment if there is a particular eyesore you need to block, (E.G. a dog house where the dog makes a real mess of things).
I hope this helps.