A common theme is adaptation. The OC gamer has to adapt to the Inuyasha world which is very different from their own. Another theme is power - using their gaming skills to gain power or an advantage. For example, knowledge of game mechanics might translate to combat skills in the Inuyasha universe.
Well, the idea of progression is big. Just like in a game, the OC in these fanfictions often goes through a form of progression. It could be in terms of power, knowledge or social standing within the Inuyasha world. Another theme is discovery. The OC discovers new things about the Inuyasha world, its magic, and its inhabitants. This discovery process is often intertwined with their own growth as a character, as they learn from their experiences and interactions in this new and strange world.
Chapter 942, "In Which Year Did the River Moon First Shine on People [Extra · River Moon Edition]", is the clearest early answer because it turns Shine's situation into a concrete plot event. The chapter gives readers a real answer by opening on She never expected Jiang Yan meant this.
Chapter 595, "Four-legged Black Toad", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. Early on, Jiang Li steadied himself with support, endured for a while, and then....
Chapter 4 is the strongest chapter-level answer because it starts from Qiao regretted her words as soon as they left her mouth. and follows through on A little girl acting mysterious, learning fortune-telling, what is this....
Chapter 922, "The Good Deed You Did!", is the clearest early answer because it turns Rong Ya's situation into a concrete plot event. It opens with Jiang Li skipped through those comments and called Zhao Lang back.
Chapter 830, "Pinky Promise for 100 Years", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. Early on, At eight o'clock in the evening, Jiang Li arrived home.. By the end, Immediately, two shadows darted out from the room inside, each....
The best chapter pointer here is Chapter 3, "Madam, the eldest young master has been missing for over half a month". It opens with Qiao was still annoyed at the attitude of this unknown girl when she heard... and closes on Jiang Yan, forced into a marriage with someone he did not love, had....
Chapter 657, "The Richest Man Becomes a Hardcore Fan?!", is the clearest early answer because it turns Jiang Yan's situation into a concrete plot event. Early on, Zhao Lang had arrived in the Capital in the early hours of the....
If you want the clearest chapter reference, go to Chapter 3. Early on, Qiao was still annoyed at the attitude of this unknown girl when she heard...; later, the chapter leans on She's actually Miss Jiang Li from the Jiang Family?!.
Chapter 643, "Jiang Li Dominates the Trending Searches!", is the clearest early answer because it turns Ancient Roman's situation into a concrete plot event.
Chapter 886, "Stinky Beggar", is the clearest early answer because it turns Chang Song's situation into a concrete plot event. A useful checkpoint is the way the scene starts with After speaking, Jiang Li stepped forward and said, "I'll treat this...