I gave it another shot in 'Henry Irons' mode, (ie: using the Knife as primary weapon), and I was able to complete the floor without losing any health points at any point, but it was very difficult. You'll need to have a Rocket Launcher and several rockets available, if you want to succeed. Here's how to do it:
The first room in floor 20 has no opponents, and there are doors at the top of the room, on both the left and right sides. Exit from the door on your left.
In the square room following, you will find one door on your left, four doors directly in front of you at the far end of the room, (the middle two doors are locked), and four doors to your right, ( middle two doors locked). The single door on the left is directly opposite the four doors on the right.
The door on the left opens to a small room which contains a Lightning Gun and two batteries. When you get to this room, select the Rocket Launcher, and wait for a few seconds before the locked doors open, and the Mechanoid Stormtroopers start to emerge. Aim your rocket launcher at the locked door directly across from you, closest to the top of the room. As this locked door starts to open, launch several rockets at the doorway, and duck back inside the room when you hear a Mechanoid Stormtrooper's death cry.
It is vitally important that you kill him before he can emerge through the door, because you need to have the door blocked open to retrieve the Gold Key, (the Silver Key is behind the other set of locked doors at the top of the room, but I've never been able to get those doors blocked open; the angle is too sharp). In one attempt I killed a Mechanoid Stormtrooper some distance behind the door, and it blocked the door open, even though there was no corpse in the doorway. If you do not succeed at blocking open at least one of the locked doors, you cannot complete this floor, and you won't be able to know the door is blocked until after you clear the room of approximately eight MSTs.
After firing your rockets, (I usually use 6-8 in rapid succession), duck back into the small room, and select the Knife as weapon, (yes, the Knife). It is crucial that you have the correct stabbing angle, or the first MST will come into the room, and kill you at point blank range. Be on the right side of the small room, and position yourself so that you can't see any part of the next room, because the left and right sides of the door frame overlap, and start clicking with the Knife. You don't exactly stab the MST, you stab in front of him, letting him walk into the knife thrusts. If you have the right angle, only part of his arm and head will be visible.
It takes about 75 knife thrusts to kill an MST, and three or four MSTs will follow, one after another, so expect to be clicking your left mouse button continuously for about two minutes. When no more MSTs come in for about 20 seconds, the first wave is over. Several other MSTs, however, are waiting in the room.
You next need to pop you head out briefly, to catch the attention of the MSTs still in the room, before immediately going back to your stabbing spot. I think there are five or six more MSTs in the second wave, one or two more than in the first wave. Repeat the procedure from above to dispatch these ones, (ie: about threer or four minutes of continuous Knife thrusting to kill them all). In addition, one or two of the MSTs will have entered the first room of the floor, through the door from which you entered the second room. They can also be killed with the Knife if you open that door, and wait for them to come to you, (or you can use a gun at this point).
Look across the square room. If you have successfully blocked open a locked door, you will be able to obtain the Gold Key. You need to have either the Gold Key or the Silver Key to procede further, but as mentioned above, I couldn't find any way to get the Silver Key.
btw, it is also possible to kill an UberMutant with the Knife, provided that you encounter him at the right spot. With very few exceptions, no opponents can advance or shoot if they are being stabbed, provided that a minimum portion of their body is visible to you. The more of them you can see, the more likely they can kill you first. If too much of an MST can be seen, they will just move past the Knife, and kill you quickly, at close range.