Connecting "out of system" roads? I've been trying to figure out how to connect SNOT road models that are at varying angles to one another. You can see my efforts in this thread.

Are there any interesting methods of connecting roads like these that most people might not be aware of? I read up on integer triangles, but there are none for 45 degree angles, and probably none for 30 and 60 degree angles as well.

Are there any special parts that make this possible?

See also: https://math.stackexchange.com/questions/2607147/is-there-a-pythagorean-triple-whose-angles-are-90-45-and-45-degrees

Here is an example that is fairly close, except that the road pieces are not connected to one another.
There ARE integer sided triangles that have angles of 60 or 120 degrees, see here : https://en.wikipedia.org/wiki/Eisenstein_triple but I'm not sure how this helps you for building roads.
45 degrees there indeed aren't any. 
A progress of going one stud forward one stud left will get you 45 degrees if working studs on top. In case of SNOT 2 studs forward, 5 plates will also progress in an angle of 45 degrees.
There are elements that let you progress half a plate, so 1 stud to 2.5 plates works also.
For 60 or 30 degrees, the tangent is irrational so no 'precise' or exact progression exists, but it can probably fairly well be approximated. 
There are technic pieces called angular connectors that make angles that are multiples of 22.5 degrees. Also several connectors that make multiples of 60 degrees.
Also hinges that "click" in angles of 22.5 degrees...

Update: picture of angular connectors 

you would additionally need technic axles and bricks having axle holes:


But there are lots of other ways to connect the connectors, e.g. bricks with pin holes and a half-axle pin, half pins with stud, axles with stud,...