It seems I am being "forced" to turn to America for my direct line, not just my Grandma's sister's family (which appear to be Prussian / German / Danish anyway).
My short story long: almost my entire life I have known about my great-grandfather being "of Swedish descent". This was what my mother, his granddaughter was told. This is what my Uncle, his grandson, was also told. I have a copy of his marriage certificate, in which it is stated that he was "born in Liverpool, England, in 1866, father Larsse Williamson, mother Anne Swanson".
For years my mother and I tried to find his birth in England. For years my mother and I tried to find out about his father in Sweden. We had no success on either count. The State Library of Queensland told us that Sweden's records weren't like ours (Queensland's), held in one place, but retained by the Parishes. If we knew the Parish, we could find the records. Well, we didn't have a clue about the Parish. How would we? As it turns out, we would have had no success anyway, as we were looking for a surname, when we would have needed to look for a patronymic. Even if we'd known to look for a patronymic, we would have been looking for the wrong one (due to the information we had being incorrect). Making it more difficult, or so we saw it, was that great-grand had different ages on the registrations for marriage and children, making his birth year anything from 1862 to 1869. NONE of them, as it turns out, being even close to the actuality (1857).
As recently posted to G2G, I have found the facts for the birth date AND place .. and neither has any resemblance to what was "known". Great-grand wasn't born in Liverpool, England, to Larsse Williamson and Anne Swanson (although that was probably the closest to the reality), but was actually born IN Sweden, to Waldemar Larsson and Anna Svensdotter.
Thanks to the wonderful help from Eva Ekeblad, I know that Great-grand is recorded in the "leaving book" as departing Sweden in 1880 and going "to Amerika". (Patience, please, I'm getting there.) The question then became "did he actually go to America?" with another being "IF he went to America, for how long?" .. and another "HOW did the son of a tenant farmer from Sweden end up in North Queensland, Australia, as a Teacher of Dancing?". Now I can add another to the list. "What did he actually DO in America?" Thanks to a link to a newspaper item sent to me by another Wikitreer (Sharon Weekes), it seems he may have done some tobacco farming prior to his arrival in Australia. But where? For how long? He departed Sweden in 1880. He was in Queensland getting my Great-grandmother pregnant before they married (do I hear *gasp* from the audience?) in March of 1899 (Granddad was born in October 1899).
So .. would 18 years be long enough to gain "considerable experience" in the growing of tobacco?
And, more importantly, how do I find out exactly when and where Great-grand entered America .. and then when and where he departed again? (*phew* says the audience .. she finally got to the point!)
TLDR version: How do I find out Port of Entry (and date) immigration details for 1880/1881 USA? Is there any way of tracking someone after they arrive, but before they leave? How do I find out the Port of Departure (and the date)?
Thanks to anyone who reads this far. Bigger thanks to anyone who can actually help. 
