The phenomenon of comedogenicity is related to formation of blackheads and whiteheads - some substances cause hyperkeratinization - and they are actually "comedogenic".
The main source of information on comedogenicity amiable in the internet is the table from J. Soc. Cosmet. Chem, 40, 321-333 (1989). The assessment of comedogenicity was performed using laboratory animals - rabbits. In this method (not used anymore!) the compound is applied to the ear of an animal, and after some time biopsy is made, and comedones are assessed using microscope. In 2009 EU nearly fully banned animal testing of beauty products.
Natural oils are usually mild and they rarely cause any skin irritation. According to the above paper the only (but still mildly!) irritant oils are mink oil, shark liver oil and cotton seed oil.
Peanut oil, olive oil, almond and apricot kernel possess medium comedogenic properties (2 per 5), while castor oil, chaulmoogra oil (I have never heard of it!), babassu, squalene, safflower and sunflower oil are practically non-comedogenic.
Comedogenicity may be considered, when we formulate DIY beauty products or choose oil mixes, for example for oil cleansing method.
At the moment, as I have some mild problems with comedones (I haven't unfortunately spotted the reason yet), I use predominantly sweet almond oil mix with castor oil (10% castor oil, rest sweet almond, with around 5% of argan oil, that unfortunately can be comedogenic!) for the oil cleansing method (called sometimes OCM). I don't have much experience with that method, even though I use the muslin cloth cleansing for quite a while already - but the OCM seems to be working very, very well for me.
Previously I have used an excellent mix of glyceryl cocoate and sunflower oil as a hydrophilic cleansing oil - and I also really recommend this kind of products for a fusion of make-up removing and a deep cleanse.
I think I need to start thinking about a rich in antioxidants serum soon also, it is definitely going to be home-made, and I am going to share the recipe and effects here!
(photos from wikipedia - traditional production of argan oil and Liz Earle website - muslin cloths. Those cloths are actually the ones I am using!)