You can use the context from the function, no need to use bpy.context

use elif instead of if for every case after the first one

use elif for these cases

Try running pep-8, I think it will suggest adding an extra line in between different functions. (if the old code doesn't comply to pep-8 then I leave at your discretion to decide whether to ignore this or not).

Is clskey a term used by SVN specification?

Make it a class, not a dictionary.

Using dictionaries was a wrong decision from many ears ago. Using class will also make you to not need to worry about doing .copy().

matname -> material_name.

Seems like c, cls, cla are used interchangeably. Please stick to a single notation, preferably more clear from local code point of view.

Here cla can be class_key.
c can be cls (since the class is a reserved keyword).
cls can stay as it is, if we all agree that class is something what comes form the class attribute.

cla -> class_name. To make it clear whether cls is an object with fields or just a string name of the class.

I would really like to see this long if-else split into a helper functions.

c -> style.
Keep meaning of variable clear from its name.

You can not expect that string starting with url is a valid url. For example, you can not expect that url will be followed up with ://.

Also, the URL can have credentials and other parts. To access individual parts you don't need to implement own parser. Use urllib which is a standard library of Python.

Repetition of node.getAttribute('inkscape:label')

What is this prev_layer_name about?
Intuitively, sounds more like you need a hasmap rather than comparison with previous layer, so that you don't create new layers when layer names are interleaved (aka, Layer1 Layer2 Layer1 Layer2).

Move is a wrong technical term here.

This seems quite repetitive, should be easy and more clear to move to an utility function.

Also, unclear what is supposed to happen when the curve is closed and style is using fill (cu.materials.append from few lines above).

That will remove all currently orphaned data which might be there before the import is run. The operator should not touch anything it is not operating on.