How long does it take gravity to effect the universe?

good question but the amazing thing is it will take exactly the speed of light for the gravity to be felt.this is because gravity doesnt have rest mass and so just like light photons,it travels at c.

If the current understanding of gravity is to be assumed correct.
then it is caused by a type of field given from quantum field theory called a Higgs field.
This Higgs field interacts with a currently hypothetical force carrying particle called the Higgs Boson in order to impart mass onto other types of particle.
Currently, the Higgs field is predicted to interact with the Higgs boson in the same way that the electromagnetic and weak nuclear forces in quantum field theory interact with their respective bosons(W boson and photon), i.e. at the speed of light.

more details can be found at wikipedia

Gravity travels at the speed of light.

Gravity will be affected local to the new body in space at the speed of light and perhaps even beyond that if applying the Higg's field/ZPE field which seems to be outside of normal physics. Instincts say it will be outside of normal local physics.

But it will also follow the inverse square law. So depending on how big it is will affect tidal conditions and tectonics based on mass.
If it's a planet we 'might feel' something from it, but it may be very negligible. We don't feel any tugs from other planets or do we? I haven't seen anything that suggests that the planets exterior to our own are responsible for tides and tectonic shifts or magnetic pole influences. The moon and Sun do obviously. Planetary resonances are there because of interconnections, so there is a definite connection between our solar system's planets.

The inverse square law, will probably ensure that we are not totally overwhelmed by this new object. Would the moon be affected? Maybe a little more since it is a distance away from us.

Since everything is connected, a new planet would influence us through the other parts of the system. The moon being affected and then in turn affecting us. Probably negligible in how much though.

A body which moves freely through the solar system, not taking up residence in any orbit, will affect all planets as it passes through the system. More devastating obviously.