Interesting quest. Getting a full timeline of a building would honestly take a lot of detective work, but the easiest way to get a good overview is looking at the US census. Ancestry.com has the 1880 and the 1940 census online for free (click on the appropriate collection from the list at the bottom of the screen). You can sign up for a free 2-week trial and get access to the other census years if you'd like--just be sure to cancel before the 2 weeks are up so you aren't charged.

Once you select a census, click on it and use the browse function that's set at the right side of the page. The search function in the middle of the page is designed to find people, not geographic neighborhoods, so it's not very useful in this situation (unless you actually happen to know a name of a former tenant).

The smallest division of most censuses on Ancestry is by enumeration district. As I understand it, enumeration districts were simply how the census takers divided up the map when they went door-to-door taking the census. A few weeks back someone pointed out this site in helping figure out enumeration districts, but I haven't had much chance to see if it works very well for myself, but you may find it helpful. Once you've figured out the right enumeration district and you start browsing through census images, you'll usually see handwritten notes in the left margin of street names or house numbers and hopefully you'll recognize your own buildings. Building numbers don't typically change much. The households are generally arranged geographically so generally next-door neighbors will show up next to each other on the census.

As to whether or not the building was occupied by a brothel or not, that's a bit tougher to figure out. A census household of five or six unmarried women with different surnames all living in the same house is pretty unusual, and it's not a smoking gun that, yes, that was a brothel, but it's evidence that it was one.

Another good place to look are in city directories (like old copies of the yellowpages), but there's no one-stop comprehensive collection of city directories anywhere like there is for the census. Ancestry has a decent city directories collection which is only available by subscription. Things like googlebooks or archive.org sometimes have directories.

If you want to learn more about your building, I'd check out your local historical society. The one in my own city has a little section in their research room dedicated solely to patrons wanting to know the history of their house. They have city maps and directories and other good reference tools. I bet any sizable city with an active historical society probably has something similar set up to accommodate patrons inquiring about buildings.

Well I would recommend looking up the assessment records here†:

http://web.multco.us/assessment-taxation

(the http://www.MultCoPropTax.org link )

But unfortunately it has a $150 subscription fee (any other jurisdiction I've looked at had free access). Perhaps a realtor or loan officer could/would give you copies of the records for your building.

Also: talk to any old people you see in your neighborhood.

†Edit: I really misread your question and thought you wanted to find out if it was a warehouse. Assessment records might still be somewhat helpful by implication; for example, it's said that in Seattle the prostitutes often reported themselves as seamstresses for tax purposes. Anyway, even more reason to talk to old people.

It may not be possible to get really good information online. The historical societies may know something. But the actual original records and correspondence that might give you your answer are not that far away: 1800 SW 6th Ave. The City Auditor in suite 505 handles the municipal records. If you like, there's even an electronic search function but I don't know how good it is. You should be able to go there and see the material yourself if you want, but some things may be digitally accessible or scannable. As with all things Oregon, I suspect they're very friendly to researchers. We had one student actually go there while researching the Black Power movement in Portland and Seattle (yes, really!) and he was happy with his experience.

Police and court records might have information regarding the building's activities, and even give you some names. Old newspapers might too, if any are searchable online via Readex or another digital service. But other online sources are likely to be circumstantial at best.

Your local library can be a great resource for this type of research. Also, the Portland Resource/Records Counter looks promising: http://www.portlandoregon.gov/bds/36663

Thanks so much guys.

I will look into all of these suggestions and hopefully I will get some results to post.