Way I see it, the big hurdle here is eliminating independent Texas, since its independence and later annexation into the US is what led to war (or at least, gave the US an excuse to justify their DoW). With a 1821 PoD, I could see a few things.
First, their presence in the area can be weakened. By 1821, Moses Austin had namaged to strike a deal to bring American settlers into Texas, but Mexico's independence made it void. Moses died in 1821 itself, so his son Stephen picked that up. If you can have Stephen either not do this, or fail to renew the deal (which had to be done twice as the fall of the First Empire made the deal void again), then you can lessen American presence in Texas. This can be helped if likewise the Empresario System of 1824 is avoided, or it's not dominated almost exclusively by Americans. Or enforce the settlers assimilate, or enforce the travel ban of 1830. As it is, American presence in Texas is impossible to avoid, but it can be made as not as big as OTL to become a big problem.
Alternatively, or concurrently, Mexico needs to be set on a path that avoids the instability that plagued it during its first decades after independence. Even with no Texas, the US might still find another way to declare war, specially if it considers Mexico an easy target. Perhaps a surviving First Empire, or a Republic that avoids souring relations with the Native Americans in the north, avoids the Federalists vs Centralists conflict, avoids lagging behind in military prowess, avoids its inability to populate the north, and then that could make the prospect of war against them to be less appealing.
All in all, sticking to a 1821 PoD, then making the Empire survive and thrive could be the way to go. Something that avoids Iturbide either taking the throne, or something that avoids him dissolving Congress (in my opinion, this was what begun the whole downwards spiral), and then things could transition into a way to avoid Texas breaking off, and to deny other ways the US could take advantage of to obtain land.
Regarding that side-note about Cuba, I would think it depends. A US that is unable to expand into Mexico, will have to expand elsewhere to appease Southerners. The Caribbean is the logical route, but an earlier Kansas-Nebraska Act could do as well, although that does not necessarily exclude the former from potentially happening.
The Oregon thing can just go as OTL.