Your OC could be a ranger who has a vendetta against a powerful orc chieftain. The orc has been raiding villages and killing innocents. The OC sets out on a mission to hunt down the orc. Along the way, they get involved in a larger conflict between the forces of good and evil. They meet other characters from the Lord of the Rings world, like Aragorn or Legolas. This plot allows for a lot of action and character development as the OC battles their personal enemy while also contributing to the greater fight against Sauron.
One idea could be that the OC is a healer who joins Aragorn's journey. They meet during a battle where Aragorn is injured and the OC uses their unique healing skills to save him. This starts a bond between them as they travel together, with the OC providing medical aid to the whole fellowship.
One idea could be an OC who is a descendant of an ancient elven line with a natural resistance to the One Ring's corruption. They could be on a quest to understand their heritage and end up being drawn into the events surrounding the Ring.
One idea could be creating an original character who is a lost heir to one of the kingdoms in Middle - earth. This character could have been hidden away during a great war and now emerges to reclaim their rightful place. Another idea is an OC who is a skilled ranger from a previously unheard - of tribe in the forests. They could cross paths with the Fellowship and offer their unique skills to the cause.
For an Inuyasha male OC fanfiction plot, consider this. The male OC is an artist who can paint things that come to life. He gets caught up in the chaos around the Shikon Jewel when one of his paintings accidentally becomes a powerful demon. Now he has to work with Inuyasha and the others to defeat it. Or he could be a demon slayer who has a personal vendetta against a particular type of demon that is also involved in the Shikon Jewel saga. His presence disrupts the group's dynamics at first, but they soon realize they need his skills. Another idea is that he's a messenger from another dimension who brings news of a greater threat that will affect not only the Inuyasha world but also other dimensions.
Maybe the female elf OC is a healer. She comes across a wounded character from the Lord of the Rings world. As she nurses him back to health, they start to bond. They then journey together to find a rare herb that can cure a deadly disease spreading in Middle - earth. Along the way, they face orcs and other perils, and their relationship deepens.
Well, in some 'OC x The Lord of the Rings fanfiction', the OC could be an elf from a different part of Middle - earth that has a different culture and set of abilities. This OC might meet Legolas and they form a bond while sharing their respective elven knowledge. Also, there are fanfictions where the OC is a dwarf with a special talent for forging unique weapons that could potentially change the course of the war. And of course, there are stories where the OC is a human with a mysterious past that is somehow linked to the One Ring.
A good plot could involve a human OC who is a doctor. They end up treating a ghoul who was severely injured in a fight. This starts a strange relationship where they try to understand the nature of ghouls better. As they get more involved, they learn about a secret organization within the ghoul world that is planning something big that could endanger all of Tokyo. The OC then has to decide whether to stay out of it or try to stop it. It's a plot full of moral dilemmas and action. Also, a plot where the human OC is an artist and they use their art to show the hidden side of the ghoul - human relationship could be interesting. Their art could either be a way to promote peace or it could stir up more trouble depending on how different groups react to it.
A male OC could be a Muggle - born who discovers he has a special power that the wizarding world has never seen before. He could be hunted by dark forces who want to use his power for evil, and he has to rely on his new friends at Hogwarts to protect him. Another idea is that the male OC is a transfer student from a foreign wizarding school. He brings with him different magical techniques and cultural beliefs, which causes a stir at Hogwarts as students and teachers alike are both intrigued and a bit skeptical.
One plot idea could be that the male OC is a new student at True Cross Academy. He's a bit of an outcast because of his mysterious past. As he tries to fit in, he discovers a hidden plot within the academy that involves demons. Another idea is that he has a special power that the exorcist order wants to use for their own purposes, but he has to decide whether to cooperate or not. A third plot could be that he is on a quest to find a lost artifact that has the power to either destroy all demons or give them ultimate power, and he has to face many challenges along the way.
Here's a plot idea. The male OC is an alchemist who has a special connection to the Truth. He starts having visions of a coming catastrophe that is related to the misuse of alchemy. He has to convince the other alchemists, including Edward and Alphonse, that this is real and they need to work together to prevent it. This could involve him traveling across the country, facing various challenges and enemies along the way. Another plot could be that he's a foreign alchemist who comes to Amestris to study their alchemy. But he soon realizes that there are dark secrets within the Amestrian alchemical community that he must expose.