If the Queen is still alive when Harry has children - and he is married when he does so - Lords and Ladies, as per the Letters Patent issued by King George V in 1917, and still in force today.
They would be styled as Lord X of Wales, and Lady X of Wales for a girl (the great-grandchild of the Sovereign becomes Lord/Lady X of Y where Y is their father's territorial designation.)
Since Harry is Prince Henry of Wales and doesn't have a 'territorial designation' (i.e. a duchy/marquessate/earldom/barony of his own), they will become 'Wales'.
However, if William has children while the Queen is still alive, they will become Lord X and Lady X of Cambridge, since their father is the Duke of Cambridge. They are still Lords and Ladies as great-grandchildren of the British Sovereign). To confuse the issue, the eldest son of the eldest son of the Prince of Wales is a Prince by the same Letters Patent.
This means that the eldest of William's sons will be a Prince, but if he has any other sons, they will be Lords, and to confuse the issue even further, the eldest son of William would be His Royal Highness Prince X of Cambridge. If Charles is King by the time this happens, William's eldest son would be HRH X of Wales.
If he is unmarried and has children, they will legally be bastards and won't receive a title.
If the Queen is dead by the time Harry marries and has children, they will be princes and princesses from birth, as grandsons of the reigning Sovereign (who would be Prince Charles, presumably as George VII due to his expressed desire not to be Charles III after the first Charles' head was cut off, and the second one had a reputation for screwing anything that moved).
If both the Queen and Charles are dead by the time Harry has children, then they will still be Lords and Ladies as the son of a Prince - because the brother of a King has no particular precedence. If Harry is created the Prince of Wales and then has kids, then the eldest son will be a Prince, and the others will be Lords or Ladies.