Flavor volatiles do vary in solubility. Fortunately, if marinating a item which is fatty (like chicken), fat soluble volatiles do seem to be picked up just fine due to the fat of the item. This works best if the ratio of marinade to items being marinated isn't too much--in other words, if the marinade volume is kept small enough where the bulk of it surrounds the food, the food isn't swimming in a lot of marinade.
Oils in marinades can be used to impart flavors of their own, and are often a reason why olive oil, toasted sesame oil, or other flavorful seed and nut oils are used. Also, lean foods can benefit from some oil in the marinade, especially if the idea is to remove them and put them virtually straight onto the grill. I use evoo in most shrimp marinades because, aside from imparting its flavor, which it does, I can remove the shrimp from the marinade, skewer, then immediately grill--without the need to oil the shrimp. I don't cook them much, but I do the same for b/s chicken breasts.
Oil is, imo, a good addition to other lean meats--like pork tenderloin--but unless its flavor is required, is often not used in marinades in fattier beef cuts, and is optional in straight marinades for skin-on poultry, especially dark meat cuts. However, if the marinade in question contains significant quantities of fat soluble flavor volatiles (especially those from many herbs and spices, chilies, fresh garlic or shallot), oil can be helpful. In these situations emulsification of the marinade works best. Dijon or another prepared mustard, lecithin, xanthan or carageenan are often used in this way. This enables the flavor volatiles to truly suspend in the marinade for some time (without emulsification the oil simply separates and pools) and is the key reason why Wishbone Italian dressing or homemade emulsified vinaigrettes work well to impart flavor. Most of these marinades are liquid-predominant, i.e., the liquid volume at least meets, but usually exceeds, the volume of oil--often by a lot. (In vinaigrettes for salads, oil is predominant. Commercial salad dressings often use less oil than one would at home, and emulsify using gums; it's cheaper.)
On the other side of the spectrum, oil-based marinades that contain little or no liquid are good for vegetables meant for the grill. Evoo, say, will pick up lots of flavor from crushed garlic and lemon zest (the oil from the zest combines well with the oil in the marinade), herb flavors, etc., Because many vegetables do not absorb marinades well (eggplant slices and mushrooms are two obvious exceptions), one is looking to marinate in something that clings well enough that it will still be clinging when grilling is complete. The flavors of the marinade one tastes after cooking are mostly on the veg not in it, but because grilled vegs are cut relatively thin, the illusion of the flavors being in the veg rather than simply on is created. Oil-predominant emulsified marinades can work well here too.