This is the second part of the “Corona wants a pet bird” story. There are also some callbacks to chapter 47. Speaking of which, I'm not entirely positive about Father's line on page 177, but I'm convinced it's some kind of pun.
Of note, I think the picture Jun holds up on page 170 (by page numbers) is a reference to the Ultra Q episode 12, called “I saw a bird” (the title of the last chapter).
On the final page, there's a wall scroll reading “Dysentery”. There have been others (smallpox showed up in chapter 39). I think this is based on the pun of “hyouki” (calligraphy/inscription) against “byouki” (illness/disease). The kana for the two words only differ by some voicing marks.