Whether the air cleaner was supposed to be oil most likely depends on how dense and thick the felt is. Normally oiled filters are wrung out to ensure they only have an oil film, not a soggy mess, and wringing out felt without tearing it apart sounds difficult. If the oil was being sucked from the filter into the carburetor it sounds as if there may have been rather substantial suction going on. In other words, I suspect that filter should have been relatively dry, and that is likely to be the problem. Here is what the owner manual says:
AIR FILTER
- Every 8-10 working hours, take off the cover (A, Fig. 23) and the filter (B). The filter (B) should be cleaned by shaking it well and with a soft brush.
I can't make any sense out of that instruction if the filter is supposed to be oiled.
You probably know that trimmer is actually an Efco, made in Italy. It seems like a decent piece of equipment on a quick look. Here is the owner manual:
http://www.efcopower.com/sites/default/files/Efco_HT27.pdf