Dwarves can't legally marry.
One watt for every impure thought

This message has been deleted.

Through Declaration of Nullity for lack of consummation, similar to the "ratum sed non consummatum" of the Catholic Church.

Makes sense, but when did that happen in all the confusion? Tyrion was pretending to Tywin that he was trying to make Sansa pregnant. Then Shae told everybody that Sansa was still a virgin but promised to have sex with Tyrion if he poisoned Joffrey. Sansa was by this time in hiding and in no position to discuss her legal status. Everybody else expected for Tyrion's head to be chopped off shortly, which of course would also end the marriage. Nobody was saying "hey, we ought to annull the marriage".
My theory was the Westeros had a law saying that when a man (Tyrion) is condemned to death, he is legally dead and his wife is free to remarry ( this idea is used in Gilbert and Sullivan's MIKADO, where it is played for laughs. The MIKADO also had the line that the judge who condemns a man to death should carry out the execution, which is Ned Stark's philosophy. I suspect George Martin is familiar with the MIKADO)
The real problem, of course, is that TV!Sansa is the conflation of two different characters in the books, one of whom married Tyrion and the other married Ramsey.

It would need to be annulled by the high septon, which would never happen as he's in kings landing and under control of the Lannister until the sparrows come and the high sparrow wasn't likely to do so either.

On this planet, that isn't enough to make a marriage legally invalid, and hasn't been through much of history. In civilizations with marriage and divorce laws a lack of consummation was usually enough to get a marriage annulled, but there was always an annulment process to go through before either party was free to marry again, and which hasn't been gone through in either the books or the show.
So of course my assumption that there's a legal annulment process IS an assumption, but it's likely enough. The only reason I bring it up is in case Tyrion and Sansa meet again, if so the question of whether they're still married might be open.
Seventy-seven courses and a regicide, never a wedding like it!

There was never any declaration of nullity on the show
Yes, it was. LF made it clear to Bolton that she was a maid and, thus, her marriage was invalid. Roose didn't care one way or the other but it was made explicit that the marriage was invalid for that reason.
But it was a blink and you miss it moment.

There was never any declaration of nullity on the show, but then the Boltons never cared about laws. They could impress their subjects and bannermen with a Stark wife, so they held a wedding and a wedding night and called it a marriage, and nobody in the North objected except the bride, and her wishes didn't count.
So it's possible that her marriage to Tyrion would still be considered legally valid, in the few places left in Westeros that care about law.
Seventy-seven courses and a regicide, never a wedding like it!

You aren't stupid. It wasn't handled well in the show.

Ohhhh duh. I'm so stupid. Thank you

This message has been deleted.

Through Declaration of Nullity for lack of consummation, similar to the "ratum sed non consummatum" of the Catholic Church.

"Art is magic delivered from the lie of being truth"