Monika is likely the oldest, and must be 19

I was looking over their birthdays and realized something.

Sayori's birthday is May 11

Nastuki's birthday is July 30

Monika's birthday is September 22

Yuri's is unknown as of now.

There's a disclaimer saying all characters are 18 or older.

Natsuki says that she is the youngest. Since she was born in July, this means anyone born on a month after July must have been born the year prior. Since Monika's birthday is only a month away, it's fair to assume Yuri was born after Monika, which means yuri is younger.

This means either Sayori is the oldest by 4 months (14 months older than Natsuki), or Monika is the oldest, which seems more likely.

This means Sayori is 2 months older than Natsuki, Yuri is 7-9 months older than Natsuki, and Monika is 10 months older than Natsuki. This doesn't automatically mean Monika is 19 though, for that we have to look at when the game takes place.

Judging by Sayori's calendar, the year is 2017. Considering the month of November is scribbled out on it, this means it likely takes place in October.

This means Natsuki became 18 3 months before the game. Since Monika must be older, she must have already been 18 by the time of her birthday 1 month before the game. This means she turned 19 1 month before DDLC.

For a bit of bonus trivia. This means Monika and Yuri were born on 1998 while Sayori and Natsuki were born 1999.