Why do oblique-wing aircraft suffer from significant aerodynamic cross-coupling?
With the wing swept forward, a positive lift force on that wing will bend the wing upward and locally increase the angle of attack, especially to the outboard of a wing. The same thing happens on the wing swept backwards, only an upward deflection from lift force will reduce the local angle of attack, likewise to the greatest extent toward the wing tip where it is deflected upward the most. One wing will end up generating more lift than the other, which will require a rolling input from the aileron to cancel out. One could attempt to balance this out with different twist profiles of each wing, but that would only solve the issue in one g flight.

When, for example, the elevator is deflected to induce a positive pitching moment, the angle of attack on the wing increases and lift force increases. The increased lift generates an increased deflection of the wing. However, as outlined above, the impact on the local angle of attack due to that increased deflection is opposite between the left and right wings. This produces a coupled roll effect.

Finally, the asymmetric lift and therefore induced drag, in addition to the use the ailerons to counter this rolling tendency, will produce adverse yaw. To eliminate the sideslip you would need to use substantial rudder input, or a bank in the opposite direction of the adverse yaw induced sideslip.

Edit:

For a really simple visualization of the wing deflection inducing a local angle of attack change, take a piece of paper and hold it flat in the air in front of you, with the long edge facing you but turned away by 45 degrees (imagine you are looking at the leading edge of a 45 degree swept wing).  Bend the short end of the paper sheet that is farthest from you (the wing 'tip') upward. Your perspective is aligned with the freestream aerodynamic flow, and by bending the tip upwards you can now see the top of the outboard wing. For a normal rear swept wing this produces washout and unloads the outboard wing. Now imagine the short end of the paper sheet that is closest to you is the wing tip. Hold the wing 'root' fixed and bend the new wing tip up. The upward deflection increases the local angle of attack at the wing tip, rather than decreasing it as before for the rear swept wing.

As an aside, this is also the reason why forward swept wings are often aeroelastically unstable. An increase in the lift force produces more lift force due to the deflection, a positive feedback that can much more rapidly lead to divergent flutter!