During the opening song 'Kogarashi Sentiment' (The fourth opening in Monogatari Season 2), the video continually switches from one art style (the normal Monogatari type art), to another one (which seems like a dated art style).
Is this a homage to another artist/company who would be known for this style?
The style seems quite familiar, but that could just be the dated feel of the art.
The OP is not a parody of one series per say, but reminiscent the stereotypes of 80s/90s anime themes in general.
Kindaichi Case Files
https://www.youtube.com/watch?v=SjIXE-YWMHM
Cardcaptor Sakura
https://www.youtube.com/watch?v=UQjCFvaNwJQ
Escaflowne
https://www.youtube.com/watch?v=jbhcChdCAUk
One of the most notable parts (with the hat flying off) somewhat resembles Kimagure Orange Road and/or the Ranma 1/2 OAV OP "Love Panic" (Koi da! Panikku):
https://www.youtube.com/watch?v=777YtDfbnYI
Some sequences are a bit reminiscent of the Golden Boy OP:
