I had a similar task to do a while ago using Illustrator CS2. Names and menus etc. may have changed in the newer versions, but I'm sure you can still do the same thing. My workflow went something like this:
Add the image to be traced. Scale, rotate it etc. until it's approximately the right size and shape.
Trace the various geological contacts using the Pen tool. With each click you add a node, and by clicking and dragging you can create smooth segments. This allows you to create smooth lines with sharp discontinuities. An alternative is to use the Pen tool to click roughly along the desired line, then use the Direct Selection tool to select some or all of the line's nodes. You can then use Object > Path > Simplify to smooth just the selected part of the line. Again, this allows you to create smooth lines with sharp breaks for faults etc.
Apply any distortion tools to create your wavy lines as necessary.
Once your contacts have been traced, select them all and copy them to a new layer positioned below your original lines layer (ctrl+f will paste them into the same location as the originals). Add some additional lines to mark the boundary of your tracing (i.e. lines for the left, right and bottom edges of your section), then select all the lines in the new layer and create a Live Paint group. This is a bit like the Feature to Polygon tool in ArcGIS: it automatically identifies the polygons defined by your lines and lets you fill them using the Live Paint tool (a bucket symbol).
Once you've finished adding colours etc. you can Expand the Live Paint group. You should end up with two layers: one on top which has your contact lines and another below it which has coloured polygons representing your stratigraphic units.
Apologies if the above is a little vague - I don't have Illustrator on this computer, so I can't check the details at the moment.
It may also be worth looking at Illustrator's Live Trace function. If your hand-drawn sections are reasonably neat, then you might be able to use this to digitize the lines for you. However, if most of the sections are rough pencil sketches like in your example, it probably won't work very well.
When exporting to SVG, QGIS leverages Qt's QSvgGenerator in QgsComposer::exportCompositionAsSVG. Note the SVG Export warning dialog:
The SVG export function in QGIS has several problems due to bugs and
deficiencies in the Qt4 svg code. In particular, there are problems
with layers not being clipped to the map bounding box. If you require
a vector-based output file from Qgis it is suggested that you try
printing to PostScript if the SVG output is not satisfactory
With regards to opening the SVG directly in Illustrator, ensure that your base units in Illustrator for strokes are MM, not Points (the default), but do this prior to opening the SVG. You can also try setting the units to MM in the Document Setup if you are importing into an existing Illustrator document. These settings may not change the resultant import, though.
As you noted, Illustrator has trouble accepting the default MM units of the QGIS SVG export while Inkscape does a better job (Illustrator just doesn't seem to scale strokes at all). Therefore, you can try opening the SVG in Inkscape first, then exporting a PDF-formatted copy out. Opening the PDF copy in Illustrator should provide more accurate line width and font-rendering results than opening the SVG directly. I did not have good luck exporting to EPS from Inkscape, as it seemed to randomly rasterize parts of the output.
Likewise, you can also try exporting directly to PDF from QGIS and opening that in Illustrator. There will likely be differences in the result in Illustrator between the above SVG->Inkscape->PDF->Illustrator and PDF->Illustrator workflows. If you need more document structure, the former may be useful, though it destroys most of the SVG structure when the PDF format is introduced.
If you feel there is an issue that needs addressed here in the QGIS source code (if possible), please create a very detailed issue report, with lots of output sample comparisons, on the QGIS issue tracker. I could not find any existing issue ticket.
The best solution for SVG output in QGIS may be to create a custom exporter that is not tied to QSvgGenerator, or create a new QSvgGenerator subclass that pre-scales line widths for Illustrator-specific SVG output.
Best Answer
I would use this approach:
Since, Illustrator has it's setup as standard pages, you should first create a print composer and save the page as either an SVG or a PDF.
As, an alternative for layers, you may want to try exporting into DXF.