Good guess, there probably is a lot of sludge and rust in the bottom of that tank that was loosened when you moved it.
While that could happen, I'm thinking that is not the likely situation. Older tanks that have a dip tube several inches above the bottom have developed a sedimentary layer that compacts and becomes pretty stable over time. You would have to be pretty careless in the moving, repositioning, and installation to get that stuff up into the dip tube. It is much more likely that this would happen if an unskilled guy installed a NEW dip tube, and stuck it INTO the sediment. A good contractor would flush the tank, properly install a new tube and lineset, and install the tiger as mentioned above. Since this may not be a contractor-supervised job, I'm thinking the best reason is a kink or crush somewhere, and a clogged strainer is the second possibility.
Of course, in a cyber-diagnostic situation, we are all guessing. At a minimum, you can eliminate the line by exposing the connections at each end and see if the line is clear.
I DO recommend a good contractor be used at this point, to cover all the bases, "live and in person."
[Avatar photo from a Florida training accident. Everyone walked away.] 2 Tim 3:16-17
Check those lines. Either a leak or a kink. Do you have the lines the right distance down in the tank? That two stage pump might be the answer. (If yours system does not have one. Your pump filter might be stopped up. Has your oil filter been replaced. How is your nozzle? You might have to call an oil burner man. The oil we are getting now is not very clean. Have to change the oil filters a lot more offen than we used to. Sludge is a real problem now. In your tank, lines, in your pump filter and line filter.