What do you think of the strong nuclear force? Gluons are the force carriers between color-charged particles. And gluons themselves have a color charge. So gluons transmit force between each other. Does that mean the universe is already too strange to exist?
By the way, this is why the strong nuclear force has such a short range. Gravity has infinite range as far as we can tell, so that makes it unlikely that the graviton, if it exists, has mass.
Photon's and gravitons have to be masses because Gravity and Light and interact with matter at finite distances.
If your 1 billion light years from earth, you are still effected by the Earth's gravity (well its likely smaller then experimental error but never mind that it still exist).
So there needs to be gravitons from Earth flooding the entire sphere of space for 1 billion light years around the Earth. All these gravitons have mass, and are emitting their own gravitons. Which all have mass and energy! Where is this mass and energy coming from? It really can't, it violates the laws of thermodynamics. But so does Dark Energy so who knows.
There are two aspects to it. And I'll be very hand-wavey because QCD is not my field.
Suppose you have two quarks and you start to pull them apart. The gluons that transmit the force between the two quarks tend to "bunch" together because they have their own charge. You can think of it roughly like a rope of gluons trying to pull the quarks back together.
If you keep pulling on the quarks, you might expect the gluons to eventually "break". But this doesn't happen, because the gluons act on each other. If there were ever a break, more gluons would join in, tugging the break back together. Eventually, you end up with so much energy density in all these gluons that they start forming new quarks and other particles. These new particles will bind with your quarks and each other to form color-neutral particles.
So I spoke a little imprecisely. Gluons, being massless, have infinite range. But you won't ever see the strong force acting over any large distance because anytime you try to get color-charged particles far enough apart, you'll end up making more particles.
By the way, this is why the strong nuclear force has such a short range. Gravity has infinite range as far as we can tell, so that makes it unlikely that the graviton, if it exists, has mass.