Remove anything that arises from below the grafts (are they all visible? You should be able to see where each variety was grafted into the tree). But beyond the grafts, the only reason to remove growth is for size control, or in the case of a multi-variety tree, to keep the more vigorous types (e.g., grapefruit) from overwhelming the less vigorous types. Unless that's happening, citrus has no real need for pruning; they tend to make a well-shaped tree on their own.

Yes, the graft lines are visible and you are exactly right, the grapefruit is trying to take it over. So I pruned back the grapefruit and some of the lemon today even though there is some fruit(4 grapefruit and 6 lemons) on them(in Florida). Hope I didnt prune them too early. Can u prune any of the grafts at any time?? Thanks for the info.

Malcom-
What about the soft, flat and very rapidly growing water sprouts above the graft. Should they be removed? I have removed then as they grow very large with huge leaves.Can they produce fruit?

Any growth above the graft can produce fruit. Citrus doesn't produce water sprouts in the same sense that an apple or pear might. On the other hand, if you're trying to maintain the tree small, for a container indoors, you may want to remove the unusually vigorous branches. Outdoors, in open soil, those are desirable, since they make a bigger tree quicker.

I have the same concern as the original poster. The abnormal sprouts on my young navel orange (Lane Late Navel, about 3.5 feet tall) have THORNS on them.
The abnormal sprouts are not from the trunk or below the graft but are from other "normal" branches. They grow very fast, have wider spacing between leaves, and the stem has a distinctly flattened cross section (and they have thorns).
What causes these abnormal sprouts? Can I prevent them? Should I remove them (I don't like the thorns and I wonder about eventual fruit quality)?

They are normal and will eventually fruit. They are an attempt at fast growth, so are soft and flattened. They do turn into normal branches. I'm thrilled to see them after my trees were made into stumps after hurricanes! The trees are regrowing/reshaping themselves beautifully.

Lisa

I noticed this fast growth on my Meyer lemon and Cara Cara orange trees this year. The branches looked so weird to me, especially since I don't think they've done this in the past, but I left most of the growth intact. Glad to know it's normal.