Oh God. I had this same problem with my Corolla ('97). Let's see, if memory serves correct, it had a cracked/broken crankshaft pulley (that's a part on the engine, in case you're like me and don't know s*** 'bout cars). I don't know if your vehicle, being a 2001, has the same problem. I sure hope not, because this is a HUGE problem and EXTREMELY costly.
My car was making the same noise you're describing. A loud ticking noise. Then it progressed and got even worse. It started sounding like huge rusty, non lubricated gears were grinding the hell outta each other (my car too had oil, and all it's fluids).
I wound up having to replace the entire engine, because being Toyota, and the way the engine is built, and the parts they sell/or don't sell separately, it wasn't possible to just fix the pulley itself. Or, if we tried, there was still a problem with the engine as a whole. Anyway, long story short, I had to replace the engine at a whopping $1800!
A couple of years after that, the same issue arose AGAIN. Toyota vehicles can only run on Toyota parts, so when I originally had the engine replaced, it basically got replaced with another Toyota engine--which also had this same malfunction. This was for my model year, and several years after that they had this problem with the engines. Again though, I don't know if your model year falls into the same category.
Now, here's the clincher, Toyota is WELL AWARE of this problem. In fact, every Toyota dealership I called, told me that this is a general problem with that engine, and that they don't, nor would, correct the problem--they said they'd only replace the engine, because, there was no point in replacing a part, when the entire engine itself was what was defecting that part in the first place. I even had my guy friends ('cuz for a while I thought they were taking advantage of me since I'm female), but I had several male friends call and ask, and they were getting the same reply.
Anyway, the second time this happened to my car, I just got rid of it. Thankfully I was in a place where I could do that. I don't know how bad yours is yet or what your situation is, but I can only tell you, if it's the same issue as mine, you're in for a lot of trouble with that. If you like, you can email me and I'll try to help you and recommend stuff as best I can. I really hope your issue isn't what mine was.
For now, I'd recommend calling some Toyota dealerships in your area and ask for the service manager. Tell him you've heard about this same problem with another person, and you want to know if your model year is affected by this problem. If he says no, then he can give you some advice over the phone as to what the problem may be. If he says yes, I'd recommend finding an auto shop that you trust to get the engine replaced (if you can't afford to get rid of the vehicle altogether), as the dealership will charge you an arm and a leg. At least that'll buy you some time. ...but again, it will be expensive.
Best of luck to you. This problem sucks major ass.