Synthetic can mean many things to people: usually it means it smells of something man made or industrial, or at least has those overtones or undertones. An obvious example is something like the packaging tape note in CdG A New perfume. A less obvious example is a floral note that has an acetone like smell to it in the background - something I get for example in the scent Wicken 3000, which also has synthetic water and salt notes. Some notes are guaranteed to be synthetic since there is no natural extract available - one such example is apple. But of course, a well done synthetic apple accord will smell natural.
Sometimes, natural oils smell harsh and synthetic to people.
I've found that many people find scents that contain a large dose of natural clary sage (Versace PH, Luna Rossa, Versace Dreamer) or juniper (Dreamer again, Cooper Square) to be synthetic, specifically those notes, as they mention the synthetic-ness of the early stages/opening of the perfume, when those notes are most prominent.
I remember reading about the makers of Febreze testing various lavender scents with the public. They found that people much preferred the synthetic, sweeter and softer lavender, to the real lavender oil. Many people thought that the real lavender oil did not smell of lavender at all, simply because they've been so condition by their exposure to the synthetic, softer and sweeter fake lavenders they've smelled all their lives in products. I think this is something akin to kids who eat a lot of fast food and actually prefer a nasty McDonald's burger to a delicious home cooked meal.
Cloying just means overbearing, usually with regards to a scents sweetness. Cloying, to me, often also implies a thick texture to the scent. Thick, syrupy, very dense - the olfactory equivalent of molasses.