Hi, i have a 95 Buick park avenue that consitently hesitates at 4kRPM in drive, nuetral or Park,

The starter drive may be staying engaged. Don't start or drive it until you have it checked-out, as it could also ruin the matching teeth on the flywheel. Replacing this would require removing either the transmission or motor.

Check the TPS on the throttle body. When they start to go bad it makes the engine hesitate

Sounds like the rap relay is bad.

Get a replacement ac control head.

possibly your ball joints, or a wheel bearing starting to go

http://www.onlinefreeebooks.net/pdf-download/buick+park+avenue+service+manual/

Change the oil pressure switch then try

I think any dealer would have these on hand; if my memory is working right, these did have to be a specific class and will need to be torqued carefully to avoid stripping the female threads.  

i would check for spark and if you have that check fuel pump pressure should be around 40 psi if not check fuel pump voltage at pump connection if voltage is at battery voltage at connector it is probably yhe pump the pump is located in the fuel tank

I had hesitation problems and a tune-up and wire change solved the problem