Second Sons

[LadyAprilLucy]

Just wondering. What happened to 2nd/3rd/4th sons of aristocracy? What did they do with themselves if they had no money? Did their parents have to support them all their lives? And what about grandchildren etc?

The second son would go into the army or become a clergyman.

Disclaimer: I only know this from reading Austen not actual history books.

All sorts.
They would have an allowance - how much would vary between families. It wouldn't be huge, but would be enough to live a Bertie Woosterish existence by not paying your creditors until strictly necessary. There would be a lot of social opportunities in the season in town - parties and balls and dinners and so forth - and in the country there would be house parties and hunting and shooting and fishing. If you weren't sociable there would be your club, where you could get fed and play cards and drink and doze in a chair.
As pp said, the army and the church were popular professions - they still are for men like Prince William and Harry. If you were of a more serious disposition, you might end up an amateur scientist or historian or philanthropist or poet - much of the great work of the nineteenth century was done by gentleman amateurs. There are lots of bumbling gentleman enthusiasts in literature, rushing around planting forests or landscaping gardens, and although they're something of a cliché, their interests are plausible enough.
Running the estate was a full-time business, and although it was traditionally the purview of your father or older brother, if it was clear than he was uninterested and you were, you might end up doing the brunt of it. Other professions were also open to you if you wanted them - politics was another favourite. You might easily become an MP.
Philanthropy or local voluntary work was another traditional pastime. Most JPs and magistrates were members of the gentry or upper middle classes, as these were unpaid positions. You might well decide to set up schools or organise fetes, as much for your own entertainment as for public good. And the Bolshevik younger son is another stock figure in comic literature.
If your family was poor - and death duties meant that many aristocratic families increasingly were - you might have to work for your living. Law or academia or at a pinch tutoring or being a secretary might become necessary.
Re: grandchildren, they would gradually become less aristocratic and more upper and then upper middle class. A Duke's younger son wouldn't expect to work, but his grandson might choose to, and his great grandson would have to.