Simple and direct:
* His claims were outrageous and completely unfounded.
* The prices at that restaurant are outrageous.
* The comedian's jokes were so outrageous that some people walked out.
Adding context:
* Her outfit was outrageous for a job interview, but she landed the job anyway.
* The movie's special effects were outrageous and completely unbelievable.
* He made an outrageous offer, but I knew he wouldn't follow through with it.
Using figurative language:
* The news was outrageous, an absolute assault on our senses.
* The party was outrageous, a whirlwind of laughter and music.
* His behavior was outrageous, a complete disregard for the rules.
Adding an opinion:
* I think it's outrageous that they would even consider cutting funding for public education.
* It's outrageous how much some companies charge for basic necessities.
* I find it outrageous that they would allow such blatant discrimination.
Remember that "outrageous" can have different meanings depending on the context. It can mean shocking, excessive, or simply absurd. Choose the meaning that best fits your sentence.