Simple things first. I assume no alarms are going off, since you did not mention any, and your green oil light is on while underway.
1. If you have an external fuel-water separator (which you should have), drain or replace it.
2. While underway, open your gas filler cap and see if that clears up the problem. If so, you have a clogged breather tube to your tank.
3. While underway, at the point where power is stalling out, check your pump up bulb. If flat, you have a partially clogged pick up tube in your gas tank.
4. Run a clear plastic line from your pump up bulb to your onboard fuel water separator and see if you are getting any air bubbles in it while running.
5. Drain and check both your on board fuel-water separator and low pressure fuel filter.
6. Drain your VST. On the back starboard side of your motor, you will see a plastic tube looped around a holder. Unhook it, and look down at the base where it connects. Beside the connection is a small set screw. Use a long flat blade screwdriver to open the set screw - slowly. With the end of the hose extended downward into a clear container that will hold at least a quart of liquid, start opening the set screw. Do not open too far - if it comes out, you will need to remove the lower cowling to retrieve it. Anywhere from two to three pints of gas, and maybe some water and gunk will come out of that tube. Be patient, the last stuff to come out is usually slow, but drain out as much as you can. If there is water, or any gunk, then your fuel-water separator and low pressure fuel filter have failed and need to be replaced. At that point, you should also change out the high pressure filter which sits on top of the fuel pump and is held in place with three 5 mm screws.