I see olive oil in marinade recipes. My question is -- are oils really able to penetrate (A) vegetables such as mushrooms, brocolli, and eggplant or (B) meats? Or should marinades only contain polar substances such as water, vinegar, salt, sugar?
Marinades are exclusively a 'surface treatment'. A penetrating treatment is a brine, and you will not use oils, but rather ingredients like salt, sugar, vinegar etc. which do produce a 'polarity' allowing it to penetrate deeply into the meat. (polarity, if I take your meaning correctly in this context, refers to the ionization of the solution allowing the brine to penetrate by way of osmosis)
So, you correctly observe that oils are not going to penetrate, but are off course with the expectation that a marinade is designed to penetrate. Now, it should be noted that these two words are often used interchangeably, however incorrect it may be.
For a deeper dive into this topic see: What is the theory of a meat marinade?
A later comment from @Cascabel prompted some additional research that warranted an edit. There are four related terms which are often used interchangeably in various contexts. Given the lack of an international governing body of food terms (ie 'The Food Police') there is no perfect authority or true consensus about the 'exact' meaning of these terms, but I have found a 'reasonably' (IMHO) consistent approach to what to call it when you soak food in liquid prior to cooking it.
Marinate (v) - To soak meat or fish in a liquid (called a marinade (n)) for the purpose of seasoning or coating the surface.
Brining (v) - To soak meat or poultry in a Brine (n) which is a high salt solution which will penetrate the meat by way of osmosis carrying additional moisture (and some flavorings) deep into the meat. (given that saltwater is an ionic solution it has a polarity to it, but this doesn't really appear to be material to the function of the solution by way of osmosis)
Maceration (v) - To soak fruits or vegetables in a solution to make them more flavorful (and digestible).
Pickling (v) soaking fruits or vegetables in a brine (n - yep, the pickling juice is referred to as a brine, and are chemically very like a meat brine) in order to add flavoring and preserve the food.
These terms are often used to cross meanings. Given that they reasonably convey the (generally) correct meaning, these distinctions are more interesting (IMHO) than they are important. For my part, when faced with questions on Seasoned Advice I am inclined to draw out the differences as being 'more objectively accurate' than colloquially useful, which is a stated goal across the Stack Exchange.