Orsdxy

Can the speaker of the house legally rescend and invitation to the president to the state of the union? If the speaker merely postpones, is this a valid workaround if it is not legal?

The State of the Union speech is purely a tradition. There are no laws regarding it, although there may be rules within each house of Congress that address it.

The only requirement is specified in the Constitution (Article II, Section 3):

[The president] shall from time to time give to Congress information of the State of the Union and recommend to their Consideration such measures as he shall judge necessary and expedient.

How the president does this has changed over time - for a good chunk of US history, it was a letter delivered to Congress, not a speech at all. But the current traditions involve the Congress passing a joint resolution (both houses agree, but it isn't a law) scheduling a joint session, and then the Speaker of the House (presumably because it's the physically larger chamber) issuing an invitation to the President to deliver a speech (or other communication) at that time.

More details from the Congressional Research Office here: https://fas.org/sgp/crs/misc/R40132.pdf

All of which is to say, there are no requirements whatsoever on how the State of the Union is conducted, so Congress (and the Speaker specifically) can do pretty much anything they want. Likewise, there are no specific requirements whatsoever on how the President delivers it or what he addresses.

Yes. There is a moment during the SOTU where the Seargent of Arms "presents the President of the United States" to the the Speaker. This is a formal matter as no one is allowed on the House (Or Senate, but it's much to small of a chamber for the purposes of the SOTU) floor without the leadership's approval. Thus, the President must be invited and can be uninvited by the Speaker.

It should be noted that, at time of writing, the Speaker has not uninvited the President, but merely noted that it would be better to postpone until after the shutdown. This seems to be due to an abundance of caution as the Secret Service is designated security lead for the event and they are currently in a Furlough status due to the shut down. The alternative solution is to send a copy of the address to the Speaker and Senate Leadership on the date it was scheduled. The Constitution does not require the President to make a speech to the joint session, though it's been a thing since Woodrow Wilson. Letters were common way of delivering the address. It's also not a time constrained event, as the Constitution is mum on the exact time, other than he should do it several times during his administration. Annual is just something everyone thought was a good idea.

According to the articles I've seen, she has suggested that he reschedule the address, or consider delivering it in written form.

The president has the power to convene a joint session of congress "on extraordinary occasions," so while the speaker may be able to cancel a specific event that was scheduled under her (partial?) authority, she cannot prevent the president from addressing congress altogether.

The president's ability to convene congress does not of course guarantee that people will actually attend, however, so the whole thing could quickly become very petty. This is presumably why she did not bluntly rescind any invitation she may have issued.

The obligatory constitutional quotation is from Article II, section 3:

He shall from time to time give to the Congress Information of the State of the Union...; he may, on extraordinary Occasions, convene both Houses, or either of them....