Are there any regular transportation from Odessa, Ukraine to the Moldovian independent republic of Transnistria? To be more exact, to Tiraspol?
Do you need a visa to get there?
There's a direct train from Odessa to Tiraspol, Transnistria, though you might not be let off, as there might not be a way to get a visa upon entry. The train continues to Chisinau, Moldova, from where you can backtrack to Transnistria.
There are actually great many options for getting to Tiraspol from Odessa including direct buses. You can see schedule (Russian) that lists 3 direct buses from Tiraspol to Odessa with the same schedule on the official Tiraspol's bus station site(Russian), with reciprocal schedule from Odessa and same again in Russian
The question of visa is a bit interesting with Transnistria being such a contested territory but the Russian Wikivoyage page provides some of the better information on the visa requirements, which are somewhat weird.