This is my solo strategy for Call of Duty: Black Ops Zombies Mode's map, Kino der Toten. I hope it helps.
Round 1 - Buy the Quick Revive first before a weapon. Shoot each zombie four times then knife. If any zombie happens to get out of a barricade, shoot it to death. Knifing zombies that have broken in is unwise because knifing will make you automatically receive a power-up that it drops, which is a waste of potential.
Round 2 - Buy the M14, because it has more ammo and gets more points because it's weaker than the Olympia. If you still have ammo for the M1911, use a whole magazine on each zombie then knife. When you run out, use the M14 to shoot each zombie once then knife. If zombies break in and there are still many, shoot each zombie twice. When you're down to the last zombie, shoot once then knife.
Round 3 - Shoot each zombie twice then knife. If there are many zombies, shoot normally without knifing, unless you trust your sprinting skills.
Round 4 - Shoot each zombie thrice then knife. When many zombies break in, go to the first door up the stairs and keep your back to it. Shoot as many zombies as you can and throw frags down the stairs.When they're almost gonna get to you, keep shooting and buy the door behind you, facing the zombies and walking backwards into the next room. Check if the box is there. If it is, open it until you get an automatic weapon, shot gun or wonder weapon (except Monkey Bombs). Continue to defend yourself.
Rounds 5-10 - If you found the Random Weapon box in Round 4, continue to buy weapons until you either run out of points or get an LMG, wonder weapon, Monkey Bombs, or Teddy Bear. If not, buy the doors going to the theater or at least until you find the box (if you got the teddy bear don't forget to chect the first room first). Keep using the box until you get any of the mentioned items. The best priority for me would be the Ray Gun, because of its versatility and convenience. It's light, it's usable when you're downed, it has a large capacity, it's automatic, and it creates explosions and crawlers. Thundergun's a good choice too. When the Hellhounds appear, camp in an area where you can easily react to them. Reload all your weapons then get the Max Ammo.
Rounds 11-20 - You must be back stage by now. Camp there for a while, then only open the power when overrun. Quickly initiate the link to the pad (don't worry, if it's red it's still linkable), then run into the first room through the door the stage is facing, then link the teleporter. Aim at the right side of the door you went through, because that's where all the zombies will pass. Kill them, and if you get overrun, take the right staircase and go upstairs, until you reach the stage again. The best priority is Juggernog and not Pack-a-Punch, because these high levels will have a lot of potential attacks from behind. After each round, stay in the teleporter, fighting zombies until you get hit, then teleport. When you're in the Pack-a-Punch room, upgrade your best weapon or any good weapon that's almost out of ammo (disregard if setup is optimal), and throw frags out the window. It is also advisable to use the Ray Gun from here. When you get back, aim at the right of the door again and shoot them. When they get too close or if you get hit, run up the stairs and do the cycle again, setting up electro-shock defenses as you pass. There should be crawlers (or at least one Gas Zombie), so link the teleporters while they are trying to get to you. Don't forget to buy Speed Cola. It's honorable. Also, buy Revive Soda/Quick Revive every time you lose it. Save points so if you run out of ammo, you can easily buy new weapons and upgrade them, or if you get downed, you can buy all your perks again.
Rounds 20-30 - Do the same procedure as above. Use all the traps when you need to, and don't open the left side of the map unless you need to get another weapon or a better weapon. If it's in a room you already opened, buy it until you get a Wonder Weapon, LMG, or Monkey Bomb. Upgrade any Wonder Weapon or LMG that you have. Only trade your good weapons out during an emergency ammo requirement. Continue to farm points.
Rounds 31+ - You must be running out of ammo by now. Trust your instincts, buy doors, buy traps, buy weapons, upgrade them, and survive for as long as possible.