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It might be an ugly url but the content is still on your domain. In the question above it's about the image on their domain vs on the CDN's domain.
PS: didn't mean to hijack this question, I am also very interested to know the answer for the same question 
Its a google domain they use it for youtube . from the name I would assume it has something to do with images on youtube
IT could be an on-page redirect . Open up your index file equivalent and look for something like
Header( "Location: http://servicioshosting.com/" );
The is nothing wrong with having a site with no images . One of my favorite site Hacker News has none ( http://news.ycombinator.com/ ) ( ignore the logo wont you )
that said .. I would ask them why they want to have a website with no images. Talk to them about the advantages for users / how you can optimize the site for images.
If you site is structured such that the urls contain the categories you wish to sort , you can use something like Screaming Frog ( http://www.screamingfrog.co.uk/seo-spider/ ) and export all the urls and sort them out via excel in to categories and go that way
NOTE : the free version has a 500 url limit, so you might want to look at paid ( ask them if it can handle 17,00 urls before getting it ) or look at http://home.snafu.de/tilman/xenulink.html ( I haven't used it myself , so don't know if you can export stuff to excel from there )
Good luck mate , sounds like you have a big job ahead of you.
Its a bit technical but you can go through this https://developers.google.com/webmasters/ajax-crawling/ to make sure the dynamic page that you generate is actually indexable by Google.
That said 5000+ products infinite scroll is a bit scary and I would look at using rel=next and rel=prev for the pagination ( http://googlewebmastercentral.blogspot.com.au/2011/09/pagination-with-relnext-and-relprev.html )
I am not too sure what you mean by " internally linked to from the browsing results pages in the category structure: e.g. Blue Widgets, Widgets Under $250, etc. "
If you are referring to ability for users to sort through those products by picking one of the options like Blue Widgets, Widgets Under $250, etc. I would suggest rel canonical those pages to the base page . This should get you started http://support.google.com/webmasters/bin/answer.py?hl=en&answer=139394