There are various taxes .. sales taxes, excise taxes, payroll taxes, value added taxes, income taxes, etc.,
Each jurisdiction may have differing requirements.
Does bitmit (bitmit.net) pay taxes?
If sale taxes or VAT are applicable, it might be up to the individual selling through BitMit to collect them, but BitMit probably has no responsibility to interfere. For sites like eBay with auctions, many of the sellers are individuals, these are personal sales (e.g.,, as a hobby, not as a business). To help ensure that larger sellers are booking revenues, compliance efforts occur through reporting by the payment networks (e.g., PayPal). With Bitcoin, visibility to a centralized payment system is not possible.
What about a site like odesk - for freelancers - that used only bitcoins but had no comissions and got no profits. Would it have to pay taxes?
The method of payment wouldn't change whether or not taxes are due. The use of bitcoin can make it harder for a tax authority to know if all applicable taxes were being paid but it doesn't remove the tax obligation if one were to exist.
Please discuss legallity and illegality issues of running a website that uses only bitcoins./quote]
That's like asking please discuss legality and illegality issues of running a store that uses only accepts cash for purchases.