I don't think struts will have much of an effect on moving the vehicle side to side unless you really mean it's bouncing up and down when you're pushing it. Struts work in the vertical dimension. Maybe you mean it's see-sawing side to side more than you'd expect.
The MDX is taller with a higher center of gravity and a heavier vehicle than a TLX so it's going to behave a little differently when trying to rock it side to side - i.e. the movement sb more pronounced in the MDX.
A strut can go bad without leaking. There can be problems with internally leaking seals and with the external bushings that might get torn or worn and compressed (thereby being more loose).
If you know of another MDX you can bounce around you might be able to push on it and compare the two. A good experienced mechanic familiar with the MDX model might also be able to tell if a strut is faulty or not.
Alternatively, depending on age an mileage and how long you plan to keep the vehicle you could just replace the struts anyway. My 2014 has about 105K miles and the struts still behave fine but if I suspected them and if I was planning to keep the vehicle to 200K miles or more then it's possible I might decide to just replace them proactively/preventatively to then not touch them for another 100K miles. Strut replacement is expensive though so I wouldn't just casually replace them out of hope that it's whatever problem you think you're having.
The MDX is taller with a higher center of gravity and a heavier vehicle than a TLX so it's going to behave a little differently when trying to rock it side to side - i.e. the movement sb more pronounced in the MDX.
A strut can go bad without leaking. There can be problems with internally leaking seals and with the external bushings that might get torn or worn and compressed (thereby being more loose).
If you know of another MDX you can bounce around you might be able to push on it and compare the two. A good experienced mechanic familiar with the MDX model might also be able to tell if a strut is faulty or not.
Alternatively, depending on age an mileage and how long you plan to keep the vehicle you could just replace the struts anyway. My 2014 has about 105K miles and the struts still behave fine but if I suspected them and if I was planning to keep the vehicle to 200K miles or more then it's possible I might decide to just replace them proactively/preventatively to then not touch them for another 100K miles. Strut replacement is expensive though so I wouldn't just casually replace them out of hope that it's whatever problem you think you're having.