Our 2005 S80 2.5T has displayed an occasional fuel gauge error for the last three or four years. When it occurs it is always immediately after a fill-up. Upon starting up the engine to pull away from the pump, the gauge will read empty or the same level that it read before the fill-up. I can drive, turn, stop, go, (slosh gas) and the gauge remains in error. But once I kill the ignition and restart it, the gauge reads properly. And it will continue to read properly over the entire fuel burn-down which could be weeks. At the next fill-up the problem may repeat or the gauge may read properly from the first start up. More times than not it will work properly.

Apparently there are two pick up units in the tank due to the "saddle" design of the tank. The following link leads to a discussion between people with the same kind of issues. It sounds like a good Vida-Dice or dealer provided read out may be necessary in order to determine which sender may be at fault:

http://forums.swedespeed.com/showthread.php?135445-Fuel-Level-Sender

As for the poor running, that sounds like a separate issue. Have you tried connecting a fuel pressure gauge to the rail and taping it to the windshield so that you can monitor pressure while actually driving under load/acceleration? That was the only way I was able to detect a bad fuel pressure sensor when the car was stuttering under hard acceleration but no check engine light. Here again, a good fault scan be be beneficial.

BTW - the turbos and non turbos use different Bosch pressure sensors. One uses a black one and one uses a gray one but I don't recall which is which nor do I know the P/Ns off hand. That is one of the parts that I would replace with only an OE Bosch rather than an aftermarket knock off. There was a recall on some of the cars for faulty pressure sensors. A call to Volvo will tell you if your VIN is eligible for a one-time replacement. Our S80 wasn't, even though it uses the same P/N as those that WERE eligible - go figure.

Good luck and let us know how it turns out, as this seems to be a common issue.
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Current rides: 2005 Volvo S80 2.5T, 2003 Volvo V70 2.4NA, 1973 Volvo 1800ES (fixed the brake fluid leak - now on to the ignition)