The phrase curiouser and curiouser means increasingly strange.

This phrase alludes to the following passage from Alice’s Adventures in Wonderland (London: Macmillan & Co., 1865), by the English author Lewis Carroll (Charles Lutwidge Dodgson – 1832-1898):

“Curiouser and curiouser!” cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English); “now I’m opening out like the largest telescope that ever was! Good-bye, feet!” (for when she looked down at her feet, they seemed to be almost out of sight, they were getting so far off) “Oh, my poor little feet, I wonder who will put on your shoes and stockings for you now, dears? I’m sure I shan’t be able! I shall be a great deal too far off to trouble myself about you: you must manage the best way you can;—but I must be kind to them,” thought Alice, “or perhaps they won’t walk the way I want to go! Let me see: I’ll give them a new pair of boots every Christmas.”

The earliest occurrences of the phrase curiouser and curiouser that I have found are from three novels by the Irish author Margaret Wolfe Hungerford (née Hamilton – 1855-1897):

1-: From Molly Bawn (Leipzig: Bernhard Tauchnitz, 1878)—Cecil misquotes the passage from Alice’s Adventures in Wonderland, since he says “‘“Curiouser and curiouser,” said Alice.’” instead of “‘“Curiouser and curiouser!” cried Alice.’”:

“My dear, how long you have been!” says Cecil, when at length Molly returns to her room. “I thought you were never coming. Where have you been?”
“In the drawing-room; and, oh, Cecil! he was there. And he would keep me, asking me question after question.”
“I daresay,” says Cecil, looking her over. “That blue négligé is tremendously becoming. No doubt he has still a good many more questions he would like to put to you. And you call yourself a nice, decorous, well-behaved——”
“Don’t be silly. You have yet to hear the ‘decorous’ and thrilling part of my tale. Just as we were in the middle of a most animated discussion what do you think happened? Somebody actually came to the door and tried to open it. In an instant Tedcastle blew out both our candles and drew me behind the curtains.”
“‘“Curiouser and curiouser,” said Alice.’ I begin to think I’m in Wonderland. The plot thickens; the impropriety deepens. It grows more interesting at every word.”

2-: From Beauty’s Daughters (Philadelphia: J. B. Lippincott & Co., 1880)—the phrase curiouser and curiouser is in inverted commas, but there is no explicit reference to Alice’s Adventures in Wonderland:

“I wish you would not dance again with Blunden.”
“With whom? Blunden? Do you mean yourself? I’m sure”—in an aggrieved tone—“I haven’t danced so very often with you that you need take me to task. And, besides, I didn’t ask you.”
There is sufficient truth in all this to irritate him.
“Nonsense,” he says, a little brusquely. “You know I mean Sir John.”
“I know nothing, except that you always talk conundrums, and they are very wearying to the constitution. I, for one, never guessed one in my life. So you may as well tell me the answer to this: Why am I not to dance with Sir John?”
“After all that has passed,”—meaningly,—“I think it will be as well for you not to do so.”
“Dear Mr. Blunden, you grow ‘curiouser and curiouser.’ Why, positively that stupid Sphinx was nothing to you.”

3-: From Portia; Or, “By Passions Rocked”, as published in Time: A Monthly Miscellany of Interesting and Amusing Literature (London: Kelly & Co.) of April 1882—the phrase curiouser and curiouser is in quotation marks, and there is an explicit reference to Alice’s Adventures in Wonderland:

“Auntie Maud sent her love to you,” says Portia.
“Eh? Much obliged, I’m sure,” says Sir Christopher. “Very good of her; mine to her in return. A most estimable woman she always was, if short of nose. How she could have thrown herself away upon that little insignificant—eh?—though he was my brother—eh?”—
“She ought to have had you,” says Miss Vibart, with soft audacity.
“Eh? eh?” says Sir Christopher, plainly delighted. “Now, what a rogue!” He turns to Dulce, as he always does on every occasion, be it sweet or bitter. “You hear her, Dulce. She flatters me, eh?”
“Uncle Christopher, you are a sad, sad flirt,” says Dulce, patting his cheek. “I am glad poor Auntie Maud escaped your fascinations. You would have forgotten her in a week. Do you know what o’clock it is?—after six. Now do go up and get ready for dinner, and try to be in time for once if only to do honour to Portia. He is so irregular,” says Dulcinea, turning to Portia.
Miss Vibart, like Alice, begins to think it all “curiouser and curiouser;” yet, withal, the house seems full of love.