Transalpina is fully opened - we did it this week-end, at the Rally Camp. But take care at the working places along the route, especially in foggy conditions or during night rides.
Transfagarasan is closed until 30-th june - this is on the site of the National Roads Company. If no other problems, starting on july 1-st you could use it. And yes, the tunnel is closed not only by snow. It would be stupid not to have gates at the entrances and allow snow get inside.... In this case the snow would be protected by heat and sun and last there much much more, making the tunnel useless.... So you can't go around these barriers :)
If you cross the bariers Goatie said, in the winter, the legal problem is not so big - you could pay with the life, if avalanche strikes, or a big money penalty for the mountain rescue.... I don't think is worth it. An avalanche noise is not a thing to be sorry for not hearing it. I heard it tree times over me (in other conditions, and each time in Fagaras), so i'm really lucky - but i don't wish to repeat the experience.
In this period, the southern side of Transfagarasan, from Curtea de Arges to Piscu Negru and to the tunnel, you could do it on motobikes (maybe with cars to), taking the detour from Vidraru dam to Cumpana - on the unpaved road, on the other bank of Vidraru lake. Attention: this detour of about 10-15 km means off-road riding, so you will find mud, bumps and other stuff like this, so higher ground clearance and not so on-road tyres helps.