Sounds like you may have a steering problem (duh

)
For an easy fix, you could try changing out the power steering fluid first. If you're not mechanically inclined though, then you may just be better off taking it to a shop. Changing out all of the PS fluid involves removing the low pressure return from the pump, starting the car, and turning the wheel full left and right until all the fluid is out. You can help flush it by pouring in some new fluid as you drain it, but that may not be necessary and it would cause you to run the pump longer with no fluid in it, which is probably a bad thing in the long run. Then turn off the car, replace the hose, fill the PS pump, restart the car, and slowly turn the wheel full left and right a few times as you have someone top off the PS reservoir until it stays up at the full line.
At least that's how I've seen it done... Dunno how the pros do it but just draining the fluid out of the pump reservoir only swaps out maybe 20% of the fluid in the system. Again, if you're not comfortable doing this, have a pro do it.
Check all the hoses and power steering rack. If it's leaking, that could cause those sounds as air bubbles work through the system and the PS pump cavitates.
A bad PS pump or even an old belt could do it because when you rapidly turn the wheel, it puts a lot of strain on the PS pump and the drag on the belts increases a lot. With old fluid or a pump with bad seals, the pump could cavitate and make noise.
If you're lucky, new fluid will work. If not, then your next cheapest thing to try is replacing the power steering pump. If the hoses are leaking or cracked, replace those too. If you have to replace the whole power steering or have a leak in the power steering rack, then you're going to get stuck for a fairly hefty repair bill.
I have had a very small leak in the low pressure return side of my power steering rack for about 4 years now, and I'm not doing anything about it because it doesn't really hurt anything but it would cost about $800 to replace the rack with a refurbished unit. As it is, the only time I notice it is occasionally when turning the wheel rapidly past center when driving very slowly, the steering wheel will hang up and jerk a bit at the exact center. I can live with that, it hasn't gotten any worse in 4 years, and it leaks only a couple of drops a month so it's not worth the $800+ repair.