NOISE - Fans have SONES ratings. The lower the number, the quieter the fan. A .5 SONES fan would be as quiet as they get.

SIZE - Bathroom exhaust is a minimum of 8 ACH (air changes per hour). Calculate the cubic feet of the area (5x6x4=120 CF). If you want to change the air 8 times in hour you would have to move/remove 960 (120x8=960)cubic feet of air per hour. Fans are rated in CFM (cubic feet per minute). To determine the fan size divided the amount of cubic feet of air you want to remove in an hour (960) by 60 (minutes in an hour). So one answer would be to get 8 ACH in a 5x6x4 space you would beed a minimum 16 cfm fan (960/60=16). I think the minimum you will find with a low somes is 50 cfm.

Remember, the air you remove from the house with this fan will be replaced with unconditioned outdoor air.

You probably won't find a commercially-available exhaust fan with specs that small. And even if you did, it'd probably be pretty expensive since it'd be such a low-volume seller that the manufacturer couldn't take advantage of economy of scale for production.

One possible solution would be to construct your own exhaust system using a brushless muffin fan and ducting of your choice. A 120mm brushless fan in the 20-30cfm range would be virtually silent and can be had online for $5. Figure another $5 for a wall wart-style DC power supply (120VAC muffin fans are available but tend to be more expensive). A muffin fan with ball bearings (as opposed to sleeve bearings) should be able to run continuously for 5-10 years with no problems.

As for where to locate the fan, I'd put the fan at the source of the odor rather than on the far end of the duct.

I think it shouldn't matter where the fan is.

I personally don't know what a muffin fan is(and all I can think of is the muffin man song...) but I wonder if a computer fan would be right sized.

As far as duct goes - you should be able to use bath vent ducting. Have you considered just venting down to the basement/crawlspace. I guess it depends what you have and where you live.

Another issue is that the air has to get into this space from somewhere - I don't know if you have a door to this space or not - but if have a cat door and it is otherwise sealed, then you won't get the flow that you want without a bigger, noisier, more energy inefficient fan.

I certainly understand why you came to this forum but this is definitely an unusual topic here....

If you have a tight house, an ERV or HRV would be a beneficial addition. You could add one and put the inside intake in with the litter boxes. The air would be exhausted outside.

Google ERV and HRV to see if one of them might be a good thing for your particular home.

Even if you don't have a tight house, you could use one of these devices for the application. It would help mitigate the expense of unconditioned air infiltration that you will surely have if you vent that space 24/7.

Thanks guys, very helpful and informative. As for a cat-door to the space....well, I tried something along those lines and someone who didn't care for the idea (I still haven't identified the perp) crapped and peed on the floor. Hence, this inquiry.

I may try to exhaust the air directly into the crawl space, which is where the hole in the base of the wall would provide access to.