My 81 yo FIL came to live with us 4 weeks ago. He is refusing to shower & change his clothes, he thinks it is unreasonable of us to ask.

He he is out of his element is used to being in his own house maybe you have to get some things from his old place to make him feel comfortable at yours maybe that will help him a little going to a new place for somebody with dementia it's hard you have to get used to things all over again so get some things that would remind him of home maybe that will help

(My answer is assuming he is cognitively able to understand and remember the basics.)
If so, you will need to have a non-argumentative conversation with him. Express in very direct language that he stinks, he stinks because he is dirty, and that the situation is one that won't be tolerated. Lovingly address his reasons for not wishing to bathe. Try to find out if he has a medical or emotional, logical or even illogical reason for not wanting to shower or bathe. Does he have a skin condition hidden under his clothing that causes bathing to be painful? Is he afraid of falling due to an earlier fall in the bath that you didn't know about? Is he worried you will "steal his stuff or spy on him while he's bathing?" Does the water hurt when it hits his skin due to a sensory processing issue yet un-diagnosed? Does arthritis make the effort of removing and then replacing all his clothing extremely painful? All of these are actual reasons I have seen in elders for not wanting to bathe.
Once you have dealt with and made allowances and compromises to work with his reasons and make things less painful for him, be firm. Tell him that you will help as needed but he WILL bathe/shower at least twice a week, or once a day or whatever he needs based on his condition. You may even need to have consequences if he refuses. For Pops we made it a twice a week requirement. He has cognitive impairment, but can still mentally process immediate basics. When we tell him to bathe and he refuses, we will lock the TV and his phone until he is clean. We put a code on it and he can't watch TV or talk on phone until he is clean. Obviously, depending on your fathers mental abilities you may have to tweek the approach to suit. If his memory loss isn't profound he may even make a habit of bathing.

When is he scheduled to get an assessment? I'd keep in mind that someone who knows the facts about his behavior and abilities needs to be present with a doctor to help with the questions. Perhaps, a letter to the doctor with a list of what you are observing will help, because, he may totally provide untrue information for the assessment. My LO said that she was able to do all kinds of things that she could totally not do. So, the correct information may help.

The problem is that once a person is having significant memory loss, refusal to bathe (this is only one way they may become resistant to care), exhibiting poor judgment, etc. it's very difficult to convince them of things. Some people simply refuse to bathe or lie about bathing. My LO would swear she had just showered, but, it was a lie. The shower was dry and no damp towels. In her mind, she had done it. I'd keep in mind that once there is such cognitive decline, your FIL is not likely to be able to figure things out, like how to find an apt or long term care facility. I'd reach out to your Counsel of Aging or department of social services to see what your FIL might be qualified for. Depending on what state you are in, if he needs AL, due to dementia, he may qualify for state benefits for an AL, if his income and assets are low enough. Your county social services dept should be able to provide you information on this.

There are all kinds of ways to deal with a person with dementia to get them to bathe, but, it remains a huge deal and require a lot of time and emotional investment. I'd keep in mind that this may only be the beginning of him requiring more and more attention, as his condition progresses, he'll also likely become incontinent. Reading about the progression of dementia might help you and your husband understand what will likely be occurring down the road AND to understand that this is not him being stubborn or difficult. It's something that he cannot help. The book the 36- Hour Day is good source to check out. It's a guide to caring for people who have dementia.

You were not "obligated" to take him in. You chose to provide him with housing.

You can unchose that if he doesn't comply with your house rules.

Does he undress at night? Take his dirty clothes each night ( this is your DHs job).

Time for hubby to step up and tell dad this is a requirement for staying in your home, no bickering over it, just the way it has to be. If he’s avoiding it because he needs help in showering, then you’ll have to decide whether one of you will assist or if you’ll hire a bath aide to come in and do it. But stop asking and start requiring

I am for bluntness. This is your husbands job. He needs to tell his Dad he stinks. That he needs to shower every day. If he can't do it he may have to find some place else to live. He is living in your house, your rules.

By Pension do you mean SS? There are HUDD operated Senior buildings. They take 30% of your income for rent. Dad will have to pay electric and TV. He can get food stamps. The complex we have here is very well kept up. The transit bus comes right to the apts. Office of Aging can tell you what services they provide.

I hope you don't allow him to smoke in the house.

I would make it about me.

The lingering smell of smoke gives me headaches, could you for your love of me compromise on this.

If he just gets ugly then I suspect you will have to deal with him like you would a child, we all have to do things out of respect for others, showering on a regular basis is one of them.

You are not stuck with him, you can take him to a men's shelter if he is just dead set against having any consideration for others in the home.