In the story, it was mentioned that Reiko died young. So, who is Takashi's dad/mom and who gave birth to him/her if Reiko died young?
The backstory of Takashi's childhood and parents are explained in anime's 4th season, from episode 11-13.
Takashi's parents have already passed away, and their names were never been revealed. His mom died just after he gave birth to Takashi. His dad died few years later, before Takashi's taking elementary school (where he was already living with his relative's family). Because of this and his bad childhood experience, he became traumatic and decided to forget his childhood memory. This is the reason why there's little info about his parents.
Photo of Takashi's parents
About Reiko's child, from Japanese's Yahoo! Answers,
From 2011/3 issue of LaLa magazine (the one where Natsume's manga is serialized), Takashi told Tanuma that his grandmother (Reiko) wasn't married (but gave birth to Takashi's mother), and she didn't know her father (Takashi's grandfather). Reiko also died after she gave birth to Takashi's mother.