So im not diagnosing your problem, but it sure looks like to me that your valve cover needs a breather tube routed to a catch can or routed downward to spew oil not on the carb.
All the oil looks like it is coming from the outside of the carb?
I mean, doesn't it make sense that the outside is coated in oil and the valve breather hole is just chilling right there pointed directly at it?
The inside of the carb sure looks like it has not seen an air filter. But it sounds like you have a filter on it? please keep in mind that the cloth style washable high flow filters
NEED TO BE OILED or they will just let in tons of dirt, which I also think is another problem you are having. Pre-filter or not, those cloth high flow filters need to be oiled.
Here are a few links for what I would add to your collection
clean your engine/oil off with this
http://www.ebay.com/itm/GUNK-EB1CA-...:g:z3AAAOSwQaJXROgo&item=381587631936&vxp=mtr
use this to oil and clean your air filter
http://www.ebay.com/itm/K-N-99-5000...ash=item4176a1ac88:g:AvkAAOxybetR~sMV&vxp=mtr
google your particular aif filter and get a a 'filter wrap' for it if you are driving it in dusty conditions.
If its an "UNI" style foam filter, you will need to look into seeing if it needs oil or not. I'm not sure.
Next, I would get these things
1) 1/4" hose to put on yoru valve cover to route it downward and away from engine and carb, or to a catch can
http://www.ebay.com/itm/NEW-1-4-ID-...ash=item236bdfbef1:g:3C0AAOSw-4BXZE5j&vxp=mtr
2) buy these hose clamps or similar to actually secure your line so it wont fall off like your filter did.
http://www.ebay.com/itm/1-4-fuel-li...945352?hash=item46352e6b88:g:aLgAAOSwDuJWwe6y
These are just ideas to get you thinking.