]But then went to Adlestrop,to visit Rev.Thomas Leigh. How was he related to them?

Note there are two Thomas Leighs mentioned here, an uncle and nephew who I have distinguished by calling one:
JA's grandfather Thomas Leigh
and the other
Rev.Thomas Leigh

Jane Austen was daughter to Cassandra Leigh (Mrs. Austen)
Cassandra Leigh (Mrs. Austen) was daughter to JA's grandfather Thomas Leigh
JA's grandfather Thomas Leigh had a brother called William Leigh.
William Leigh was father to Rev.Thomas Leigh

So for those of you who have sketched it on a piece of paper you will see that Cassandra Leigh (Mrs. Austen) was Rev.Thomas Leigh's first cousin. This makes JA Rev.Thomas Leigh's first cousin once removed.

] It's quite hopeless to sort out this web of family connections.

] (But who cares, we can't remember it anyway). And then they went to Stoneigh Abbey together, because Mr Th.Leigh had inherited this great house.

The Austens cared. Passionately. They named their children after the relatives most likely to leave them an inheritance and maintained social contact with a huge number of relatives. These days most of the biographies we read about JA are catering for a generation of people to whom second cousins, great aunts and cousins-once-removed are strangers. For JA this level of connection was both close and important. It governed a great deal of her social life and inheritance patterns within her family. Remember Rev.Thomas Leigh had inherited Stoneleigh from his fifth cousin twice removed (Mary Leigh) which means that the nearest common ancestor was his great, great, great, great, great, great grandfather (imaginatively named...Thomas Leigh!).

Most peers and many gentlemen would have a copy of a baronetage/peerage (Collins was common) and/or a copy of The Landed Gentry. Until very recently in the UK if you were a certain class of person and came home and announced you had met a rather nice young man/lady called Somthing X, your mama and papa would (Walter Elliot-style) instantly say "X? Do we know the Xs dear? Darling, who are his/her people? Are they the X's of Wherever?" And would rush off to check in the appropriate book. Most members of the nobility had a very strong uunderstanding of family trees and history. Until recently most of the history taught in the UK about English Royalty was genealogically based. JA's life marked the end of an era where the most common way to come into money and power was not to make it, but to inherit it through a pattern of patriarchal inheritance or marriage.

The whole modern concept of the nuclear family has erased what JA and her charaters saw as family. Comparatively distant (to us)relations had a duty of patronage to those relations who applied. Even the names for members of the family were different. Brothers-in-law were simply new "brothers" (Wickham and Lizzie. Ugh! In fact, even Wickham and Darcy might be called brothers or brothers-in-law! Argh!!). Think about Augusta Elton's nauseating references to "my brother Mr. Suckling" (Actually her sister's husband). A step-mother was simply your mother or might be referred to as your "mother-in-law" (I know, very confusing.) Half-brothers and sisters (Like John Dashwwod and his sisters or Mrs. Grant and the Crawfords) would nearly always refer to each other as "brother" or "sister". This underlines how poor Fanny Dashwood's manners are that she considers "halfblood" to be "no relation at all".

JA referred to cousins as distant as third cousins simply as "cousins" and great, great aunts and half-aunts as "aunt". Lucy & Anne Steele were probably not that closely related to the Jennings/Palmers though Charlotte refers to Lucy as "cousin". The Elliots and the Carterets were closely enough related to have fallen out over a failure in condolence letters but distant enough never to have met (Sir Walter was "in company" with Viscount Dalrymple just once and didn't know the rest of the family).

I estimate that JA and her immediate family knew about 100 relations (very approximate) well enough to either write to/about or visit.