I have a 127mm Ektar in need of some serious cleaning. It appears to have dust on the inside (or probably fungus), and I'd like to know if there's a way to disassemble it to clean it out. Also, are pre-war Ektars coated?

http://cameraeccentric.com/html/info/kodak_4.html
Scroll down a few pages to catalog page 55.
The arrow is the direction light travels through the lens. The front group is air spaced, the rear group is cemented. The | is where the shutter or aperture when in a barrel will be.
Each group will unscrew from the shutter. Threads are standard right hand threads. Grip the shutter firmly and turn the cell counter clockwise. You may need to use a rubber strap wrench or a jar opener to grip the cell with to loosen it. They do get stuck after several years. Once you get the cells off cleaning the inside surfaces will usually be all that is necessary.

Look at one end of the lens barrel or cell. You will see a ring with notches in the outside edges. The ring unscrews but requires special tools to remove. Once the ring is removed the cell will slide out. Under the front cell will be a stop pin or another ring for the rear element. Position is critical. Count the number of turns to remove the ring(s) or measure the distance to the barrel edge with a caliper. Some Kodak barrel lens have retainer set screws or pins that are removed from the outside edge of the barrel before the ring will unscrew. If you are disassembling a barrel lens look carefully around the barrel at the edge where the sections meet for the set screw(s) or pins. Clearance between the cell and the inside edge of the metal case the cell is mounted in is around .00001 inch.

Kodak began soft coating the inside surfaces on some of its lens in the mid 1930's. Any slight tint or coloration is most likely a coating.

I perfer a heavyweight microfiber lens cleaning cloth for lens cleaning.
http://www.adorama.com/CPCML.html

I got the front element out and there's a black ring on the back, but no notches. The front ring (the one with the name and serial number) appears to be removable but it has no notches either.

Some where on this site I read of using a rubber stopper that is hollowed out. A piece of hard rubber will work also. Using either the rubber should contact the outer (front) ring only. Press down evenly and turn counter clockwise. When using a piece of hard rubber place the pressure on points 180 degrees apart. Some lens have the ring close enough to the edge of the barrel that one can use their thumbs to unscrew the ring.

As for the rear cap try a strap wrench.

Try "rubber" bumper feet (used on the ends of round chair/table legs) from the hardware store. They come in different diameters; with luck, there should be a size that will work for you. Otherwise, a rubber jar lid gripper will provide traction for unscrewing lens elements; it's a square piece of textured "rubber" about 3-4" on a side. Also hardware store, or dollar store kitchenware aisle. Sometimes it only takes a bare hand to remove lens elements. When you reinstall them, only hand tighten, but firmly; don't force anything!