If I understand your question correctly, you want to avoid 'profile' style sites, where clients stumble across your profile, and contact you for work. Here's a few 'types' of platforms where you can get work, perhaps it will help clarify where you want to focus your energy.
One could argue that's also the internet in general (put up a page, wait for people to find you). Fiverr and Zaarly are examples of that (although not really for the kind of work you're looking for). Posting your service on craigslist is another example.
While sites like oDesk, Elance have the profile component, they're certainly not limited to it. The common usage of those sites is to view jobs clients post, submit a response, and potentially get the gig. It's far less common for clients to contact freelancers directly.
Is that the process you're looking for (you browse through potential projects, contact the client for ones you like, try to get the work)? If so, there are tons of sites like that out there, and I'm sure a few searches will turn up ones at least slanted towards the kind of work you want to do.
Contest Systems: Many freelancers strongly dislike these sites, and they only work for a few types of jobs (graphic design being one of them). Here clients post a job, and freelancers post matching designs - then the client picks one winner. 99Designs and crowdSPRING are examples of this.
where people submit jobs in graphic design and where people can submit results, all without the process of an interview or a hiring system
It seems contest sites fit that requirement the best, and if you're just wanting to get used to the 'feel' of contract work, have the time, and aren't in dire need of money - it might be worth pursuing. But in that case you're doing the work without any guarantee of payment, so I wouldn't make that a serious endeavor.