Why shouldn't a Warforged be capable of being a druid, a monk, a sorcerer, a favored soul, a cleric, or a paladin? They are made up of a stone-like substance for their skeletons, and fibrous tubes that transport a blood like fluid. with some warforged being made of natural materials, and in general being rejected from society I can easily see a warforged taking refuge in the wild, and becoming a druid.
My last character for my Pen and paper D&D group was a Warforged Shaman. He had some fighter multi-class feats, and his backstory was that after being ambushed hundreds of years before the campaign he was knocked unconscious and his rune burned out. After being left in the wild of centuries the spirits of the forest had melded with his soul such that when he was reactivated he had become one with nature.
As for monks, with all the time in the world to spend meditating on their purpose, why can't a warforged be a monk?
Warforged do in fact have souls, and sentience. We aren't sure how exactly, but in the process of house cannith creating the warforged and making them independent they introduced a sentient, souled being. Warforged have souls, and in no way is it uncommon to find faith after a lifetime without it. Having a soul, the ability to think for themselves, having a religious belief, and so on would imply they have every right to be a divine class.
Favored souls are the chosen people of their deity. One might argue that a god would never choose someone new to their faith to lead their people, yet this is exactly what happened to Moses in the bible. A god can have a plan for you even if you don't believe he exists, so I see no problem with a warforged favored soul. (They should probably have a great faith story though)
A sorcerer is a being with unharnessed magical power. They have the ability, but lack the training. Warforged were intended to be warriors, so perhaps the remnants of the arcane magic that created them granted them magic abilities, but those abilities weren't tapped until later when they were needed, and could be used freely.