The coils look just like the freon coils behind your frige. On the outside, they ring the compressor and fan in a circle or square. Those are the actual compressor coils and you'll find those very easy by removing the outer unit shell.
On the inside, you have what's called the air handler - hence, those coils are called the handler coils. The only difference between those and the compressor coils is that the handler coils run vertically, just like the back of the frige, instead of in a circle or square as in the compressor case.
Think of the coils as the air conditioning and heater's radiator. Freon is pumped to the compressor, where it is compressed (well duh, LOL). The freon, once compressed, changes from an oily gas to a dry gas. But first it has to be cooled, and that's what the compressor coils do: work like a vehicle radiator to cool it to prepare for compression.
From there, the compressor sends the gas to the air handler, where it is once again cooled, this time in dry and moisture-free gas form. The air handler is actually the sending unit that blows the cold air - called a split, it is the difference between the return air temperature and the output air temperature. The nominal split temperature for maximum efficiency is 18 degrees.
If the coils are dirty, you'll lose this degree of split, spend a lot more money heating and cooling the home, and it smells bad. That's why I think you have dirty coils, rather than mildew (which is virtually undectable to the human nose except in extreme cases). You can verify this if the utility bill is higher than normal, continually climbs higher and higher the more you use the heat or air conditioner, or if the smell keeps getting worse.
If the coils are dirty:
In the AC cycle, the dirt and dust works to insulate the coils, so the gas doesn't cool fully - the forced air is warmer than it should be, so the AC works harder and longer, running hotter, so the utility bill goes up and the smell is more pronounced.
In the heat mode, the coils do almost the same thing (keep the air away from the coils), but the coils heat up and dissipate the forced heat as all that heat is lost through the transfer that allows the dirt to act as a radiator, versus the coils. Since the coils are a pourus metal (aluminum or copper in most cases), this stench invades the lines and blows through the system. You're baking filth and grease, especially from the air handler.
The other option is a pin leak in the shrader valve or compressor itself, which will bake freon on the lines slowly and freon stinks when heated. But if you haven't had to charge your freon every year, it's highly unlikely you have a pin leak or a bad shrader valve. If you have had to, your AC tech is violating environmental rules as no charging of the system is allowed if a leak is suspected.
If you really want to confirm the coils, do this:
Go down to Home Depot or some other home place and get an infrared (thermal) thermometer. They can be had for about $30.
Now, turn your AC on (not heat) to the lowest temperature on the thermostat, and let it run for about 10 minutes.
Use the thermal thermometer and measure the temperature of the air coming out of the register (vent) that is farthest away from the air handler. It should read about 60 to 67 degrees, depending on the tonage of the unit and the cubic air footage conditioned.
Now, go to where your AC filters are - AC still running, of course - and measure the temperature of the air being sucked into the air handler.
The air coming from the register should be about 18 degrees colder than the air being sucked into the return. If it is more than 10 degrees different, your compressor, evacuation fan, or run capacitor are going bad. If it is between 10 and 15 degrees, your system may need to be charged or it has dirty coils.
Like I said, your best bet to get rid of the smell AND lower the bills AND heat and cool the house better is to keep those coils clean. The commercial coil cleaners are best, but ammonia and water will do the trick with a little more elbow grease and a few more applications of the solvent.
Since you don't even know what the coils are, my money is on dirty coils, even if you have a yearly service (which is doubtful, or you'd see the coil cleaning on the service invoice). Get 'em cleaned, and 99% of your problem will go away in a day. Then clean them yearly, and have a professional company come out to service the unit once a year for about $50. Make sure you MAKE them test the split.
If you need more info or have more questions, post 'em up! I love doing this shit!
Pull out the frige and lookat the back, and you'll know what the coils look like.