None of them have a claim. You can't pass a claim through marriage. If you consider Robert a usurper then no one has a claim but Danaerys and possibly Aegon. Since Aegon does not exist it is only Daenerys.
If we say Robert took over the throne properly but his children are bastards that would mean that the succession line is within house Baretheon meaning Stannis and his daughter. After that it's Renly. Since all three are dead the claim would extinguish as the direct Baretheon line has died out. One could argue that Edrick Storm would have a claim, given that he is an acknowledged bastard of Robert and therefore legitimized or to Mya Stone since she is acknowledged as well but not legitimized. If a regency council would be totally commited to the Baratheon blood line it would have to be a cadet branch of the house, derived from a brother, daughter or cousin or whatever of Staffon Baratheon. If there are none it would go to a cadet branch of derived from a brother, daughter etc. of Ormund Baratheon and so forth. If there are none and the bastards are not considered feasible the crown would have to be offered to one of the great houses.
If we say Robert took over properly and his children are legitimate it would go the exact same way as before with the exception of Tommen, Myrcelle and Joffrey being first in line to hinherit, after that Stannis, Shireen, Renley. After that the caroussel would go round and round again. Just being a queen consort does not give you any claims on anything. Jamie being of the King's Guard can not inherit anything and sire no children. Which means that Casterly Rock, which would be the only claim to Kingship Cersei has, would pass to Tyrion making him one of the few remaining powerful lords in the Kingdom and maybe therefore being considered.
So that is the situation. As it stands the only real claimants are 1. Aegon (if he is Aegon) 2. Daenery 3. Edrick Storm 4. anybody with the power to take the crown (in that order). That is also why Littlefinger's plan would probably work out. He is already Lord Paramount of the Riverlands, would become Lord Paramount of the North upon marrying Sansa, is acting Regent of Robert Arryn and therefore Warden of the East. That gives him 3 out of 7. In the show scenario Casterly Rock would probably be given to Cersei which doesn't matter at all since she would be deposed by him anyway. Dorne doesn't matter as it lacks the strength and ressources to challenge the combined forces of North/Vale/Riverlands, the Tyrell's are all but extinct and so are the Baretheon's meaning he could probably muster the lord's of Storm's end giving him 4 out 7 with the other 3 divided. Essentially this is the situation Tyrion and Tywin Lannister created. The Vale did nothing, they submitted Storm's end after the death of Renly, they held Casterly Rock and allied with High Garden and befriended Dorne. Giving them essentially 5 out of 7.
But just to reiterate: even on the show Cersei has no claim whatsoever. No claims can pass by simply being married to someone and a queen after the death of husband and the end of her regency is basically just a queen mother, nothing more, especially if her sons had already taken other queens. As it stands now chances are that Jon will probably relinquish his claim on the Northern Kingdom once Daenery's lands, the Martells and Tyrells will support Daenery's as well. Jon will probably be able to conquer the Riverlands before Daenerys lands.
That is also what I foresee for the books. I think Jon will take the north and since I'm pretty sure the Blackfish will survive in the books will march on the Riverlands with the help of Howland Reed and retake them. Littlefinger will probably try to marry Sansa of to Harry the Heir so that she can bear his child and he can then remove him and take over. I'm not entirely sure that that will work out however... I have a feeling that she will probably play him and somehow end up with the Vale herself. Aegon will probably conquer the Storm Lands quite handily while Dorne and Highgarden will side with Daenerys and Sansa will probably marry Aegon. Would be a good match for her and she would bring the Vale, a claim to the North and being highborn plus she always wanted a proper prince. Daenery's will probably propose to Jon or Jon will marry Arianne Martell because I somehow doubt that the Sand Snakes will kill off her, her brother and her father as easily as they did in that lazy writing they call a TV Show. Then it will be a matter of sorting it out... if Aegon survives he might actually marry Dany and I somehow have a feeling that Sansa might be held to her marriage with Tyrion when he returns therefore combining the North and Dorne and the Vale and Casterly Rock (makes sense to me... north and south, east and west) while the Stormland's will probably become part of the royal domain and the Riverlands will return to the Tully's or maybe even, as in olden times, to the Iron Born to placate them and sweeten the deal of no more reaving. I don't exactly beliebe the whole barren storyline for Dany anyway... and if so... I somehow have a feeling that the prophecy will fairly easily come true north of the wall.