IS it true that a object a spinning object exerts a slightly stronger
force of gravity that a non spinning object? Since spacetime is warped
by the mass of an object, if the object is rotating then it would also
twist space time as well as warp it. Much like a ball on a bed would
would cause it to sink, but if it was spinning, the sheets would wrap
around the ball as well. Is this true? I have heard that it is of the
more viable the theories to explain dark matter.

Hello,

   Yes, this is, roughly speaking, true in general relativity. In
fact, even disregarding the "frame dragging", a spinning object has
more energy than one which is stationary, and so has a stronger
gravitational field. But- this increase is more than offset by the
classical centrifugal effects of the rotation, and so an object weighs
less on a rotating Earth (at latitudes well away from the north &
south poles) than on a static one.

So that would mean that the gravitational effects an object places on
another is based on its ENERGY - which warpsthe space, which of course
it a function of its mass and other factors (ie momentum). FRame
dragging aside. So that would also mean that if you have a very fast
moving object (ie a particle moving near the speed of light or two
neutron stars in a close decaying orbit) their warping of 3d space is
much much higher than a stationary object.

Yes, that's right. In general relativity, the metric properties of
space surrounding an enclosed region are determined by the
momentum/energy (what some people call "momenergy"; they are the
space/time components of the momenergy vector) content of that region.

The gravitational effects from spinning objects are quite complicated,
though totally negligible for any but the most extreme astronomical
objects. In fact, two spinning objects will behave gravitationally
like magnets, with the possibility for both attractive and repulsive
forces, in addition to the attractive force, which will almost always
be huge compared to the "magnetic" gravitational effects. All of this
is described by Einstein's equation that relates the curvature of
space to the "stress-energy tensor". The mathematical details are
complex and difficult to describe. The most commonly studied case is a
rotating black hole. Very weird geometrical effects occur if the black
hole is spinning fast enough (very roughly speaking, the rotational
velocity at the event horizon is close to the speed of light).

For the earth, you can safely ignore all of this, unless you put a
super precise, superconducting gyroscope in orbit around the earth and
observe it for a year looking for a totally miniscule precession (this
experiment is being done and is called Gravity Probe B).

As others have pointed out, the centrifugal force for someone standing
on the equator is not negligible.

So suppose that by some exceptionally large sequences of coincidence
and chance (or by well-applied knowledge) there is a toroidal
(doughnut shaped) solid of very densely packed material, stable enough
to avoid collapsing into a singularity. If this mass were to somehow
be rotated at a high speed along its axis, it would have an extremely
high energy, correct? And were it to not only be capable of this
rotation, but around its own circular focus (think donuts with a hula
hoop through them, the hula hoop rotating them in a circle, but also
the doughnuts spinning around where they are located on the hula
hoop). The potential energy of this object alone would be enormous,
much less its effects on our relativistic space. Add to this simply
its gravity, and the possibilities are numerous. Would there be a
point in the middle of this ring where the rules of our universe would
no longer apply? Would that space outside of our perception contain
the original super-force before the symmetry fractioning spoken of by
string theorists? What would happen to a particle/object accelerated
into the focus of this huge amount of high gravity, high energy space?
Would it gain so much mass in its acceleration that it would tip the
gravity of the structure into a collapse, or accelerate through the
loop and continue on? What if the particle is rotating in the opposite
direction? Would it be more or less energetic than a particle rotating
in the same direction as the loop?
Sorry, got lost on a rant.
Thanks for your time. 
keyrlis@gmail

Hello,

   You said:
"there is a toroidal
(doughnut shaped) solid of very densely packed material, stable enough
to avoid collapsing into a singularity."

   It's interesting to note that, regardless the structural integrity
& stability, such a body would inescapably collapse into a black hole
were its mass to be within its own Swartzchild radius. (Swartzchild
radius = radius of a mass's own event horizon)

   And yes, your spinning toroid could be endowed with a very large
kinetic energy due to its rotary motion. But there's no reason of
which I'm aware for the center point to be exceptional. In fact, if
the total mass is less than black hole critical, the center point will
actually have zero gravitational field. The spatial curvature would be
flat at that point, with zero potential energy.

   As for counter-rotating masses, their energy doesn't cancel. Energy
is a scalar quantity, meaning that it doesn't matter the direction of
motion. If there is relative motion, then there is kinetic energy.

http://www.powerballs.com/
Try this and you can feel the force yourself ;)

Yes it's true. And if the object is spinning fast enough (and is
strong enough, which i doubt, to stand the centrifugal forces exerted
by the rotation upon itself). It can create a closed timelike loop
around itself.