GhostRyder, lifting with gloves only does one thing and that is pad your hands. Using them will trash your grip strength. It really depends on what you want to do.
I was using a bar that is pretty well worn
This can be a good thing, it will teach you to use a bar with poor notches, making your hands strong.
I'm using an overhand grip with my thumb tucked under my index finger
The grip you are using is called the "hook grip" its used to make your hands stronger, it is one of the more difficult grip styles.
Ditch the thumb under the index finger and just grip it like your squeezing it. Until your hands become stronger. Thumb should be underneath bar for this. Most people use a grip technique called over/under. It allows you to hold more weight. I would use this until your grip strength improves, mainly on the heaviest of sets.
what kind of deadlift grip do you use?
I use the standard overhand grip on light sets then switch to the over / under grip for heavy sets.
Do you use gloves?
No
How can I improve my grip?
There are a lot of grip exercises to do. Pulling without wrist straps and doing all back work without straps. I do plate pinches and Captains of Crush to train my hands.
Go buy some chalk or liquid chalk or something and pull like a man. You will get some calluses from pulling like this on your hands.
Over/under grip
Hook Grip
Overhand
Plate Pinches