Quantum entanglement says that two spatially-separated particles tested for quantum spin on the same orientation will be guaranteed to produce opposite results,...
This is a crucial point, and this description does not tell the whole story. I’ll explain for photons.
The pairwise generation of entangled photons (by their spin) has a part of uncertainty. The point is that the parallel-antiparallel orientation of the two particles could point in any direction (until now we have no better conditions for the pair production). The measuring instrument (e.g. a grid), in turn, must also be oriented in any direction, no matter where by 360°. After a series of measurements we obtained a correlation between the two entangled particles. After many experiments the entanglement is assumed to be a fact. It is derived empirically and always has this statistical component. Only in some cases we measure the entanglement, in the other cases the result is unknown. In the next half-sentence you name it:
... but testing in a different orientation invalidates previous measurements performed in different orientations (for either particle).
A second measurement on the same particles makes no sense (because the measuremnt influences the particles state/orientation), so I assume, you mean that a different measurement setup would theoretically give a different result for the same state. However, the statistical number of entangled particles measured remains the same. As an example, if the correlation was found in 25% of the measurements, this will also be the case for differently rotated grids.
So the question is, how does one know whether you're testing in the same orientation? Orientation relative to what?
As said above, it does not matter (as long as the spin pairs are oriented stochastically).
I always see orientation defined as vertical or horizontal, but those are notions of directionality that only exists under the influence of a gravitational field, which is not guaranteed at all.
There isn’t any prefered orientation.
Also, especially for particles being tested with great distances between them, what might seem like straight, or parallel lines to be used as reference, might not be, due to deformations in space due to gravity.
This does not matter because of the correlation for many particles over time. What does matter is the influence of spin when approaching edges or crossing a polarizing medium. Then the entanglement is also destroyed forever, just like after a measurement.