Yes, it is wrong to omit those objects, and native speakers would not do it. It's actually not clear that it is not "I" doing the cleaning and taking if you omit them.
"I asked to clean his room" means that I asked for permission to clean his room; that is, "I" want to do the cleaning. Otherwise, the object needs to be specified: "I asked him to clean his room."
Similarly, "I demanded " implied that "I" am the subject of the infinitive, as in "I demanded to speak to a manager." Again, "I" am the one who is going to do the speaking. When demanding something of someone else, you need to change the preposition to match, as well as specifying the object: "I demanded of him to take me" or, better: "I demanded that he take me."
"Told" is a purely transitive verb, so it's completely ungrammatical to omit the object. "I told to make up" is simply incorrect and does not mean anything at all. You need to specify the object: "I told him to make up."