Each of these cases is kind of weird in biology. Let's deconstruct each of the terms and figure out whether or not they require intramembranous channels.
Straight-up diffusion is just the random movement of molecules from one area to another going to where concentration is lowest. For example, you put a dollop of red dye into a clear glass of water, and that red dye ends up spreading over time on its own through the whole glass. Diffusion describes that process, that random movement of molecules to achieve an even mixture. In cells, diffusion across membranes only occurs with small lipids like miceles. It's really as if the membrane isn't even there! However, the main thing we see with that process is that they travel across the membrane on their own! This does not require proteins by default.
Facilitated diffusion, on the other hand, gives it away in its name. Something is "facilitating" the molecule's movement across a membrane. What facilitates the movement? A protein channel. This sort of channel is important in ion and glucose transport in the body, especially, because polar and large molecules have a tough time traversing the nonpolar zone inside the cells' membranes. However, don't mix this up with active transport. Facilitated diffusion only allows movement down the concentration gradient!
Active transport gives away the answer just as easily as facilitated diffusion! Something is "actively transporting" molecules or ions from one side to another. Active transport systems are often called "pumps" because they use energy to pump molecules against their concentration gradient (this is kind of the opposite of diffusion). There are a couple types of active transport, primary and secondary, and they all use channels. Primary is when the protein, itself, uses ATP or some other energy source to directly pump ions agains a gradient (Na-K pump, H-K pump, etc.). Secondary is when you have a "pump" on one side creating a sort of "vacuum" on the inside of the cell to draw in ions and molecules from the other side. For example, the sodium-glucose cotransporter in your intestine is able to move glucose into the cell (against the gradient, so not diffusion) because of the low concentration of sodium ions created by the Na-K pump on the other side of the cell. Take away message? LOTS OF PROTEIN CHANNELS HERE.
Finally, osmosis. Osmosis is pretty tricky because of what's going on with it. It is the process by which water moves from areas with low solute concentration to areas of high solute concentration. You could see it as the "diffusion" of water. For example, if you had two glasses of water, one pure and the other very salty, and you let water flow, but not salt, the water would flow into the glass with the salt inside to balance out the concentrations on both sides. Now, you may have seen the pictures of red blood cells exploding or shrinking, and some of this is, in fact, water moving in or out of the cell without any help. However, osmosis also occurs through little channels called aquaporins, which are transport proteins for water only. So how does osmosis occur? With and without membrane proteins!