How much mass can my character move with her when teleporting? I have feats and gear removing the line of sight restriction, if that matters.
As much as you can carry.
Teleportation doesn't have any special rules on how much stuff you can carry, other than that you can't take other creatures with you unless a power or other effect explicitly grants you the ability to do so.
Note that this restriction on bringing creatures with you is inferred rather than being directly stated in the rules: there are a handful of powers that explicitly allow you to bring along other creatures (almost always adjacent allies), which implies that teleportation ordinarily would not allow that.
From the RC, p265:
Heavy Load: Double the normal load number (that is, Strength score × 20) to find a creature's heavy load, the maximum weight it can lift off the ground. While a creature is carrying more than its normal load, it is slowed. Carrying such a load requires both hands.
So if you have, for example, a Strength of 14, you can bring 280 pounds (127kg) of stuff with you, though it takes both hands and you'll be slowed (which might matter if the teleportation uses your speed, rather than a set number of squares).
Yes, the maximum drag load is even higher, but the drag text specifically says "along the ground":
Maximum Drag Load: Five times a creature's normal load (that is, Strength × 50) is the most weight it can push or drag along the ground. The creature is slowed...
I'm dubious about any arguments that someone could drag something along the floor with them when they teleport.
From the RC, p213:
Instantaneous: Teleportation takes no time. The target disappears and immediately appears in the destination that the teleporting creature chooses. The movement is unhindered by intervening creatures, objects, or terrain.