In Hinduism, what are the four levels of Vedanta?
I think that the wording of the question has to be assessed a bit. As far as I can tell in the study of Vedanta, there is not particular "levels." It is not progressive in a linear sense whereby one moves from one level to a "higher" level. The study of Vedanta is the striving to understand the Brahman, or the ultimate nature of being. This is a union between the individual and the divine. I am not sure of any particular leveling in this process. The story in the link below about how Vedanta is seen between the two birds on the tree is excellent in speaking to this point. The difference between the bird on the higher limb and the lower one is not segmented into levels. Rather, it is the bird on the lower branch who ascends higher to realize that the higher bird is them and this is the real recognition of where the bird's true nature lies. The progression between the mundane reality in this life and the acknowledgement of the universal spirit of which we are a part is where the study of Vedanta lies.
In seeking this point, there are three or four types of Yoga that are to be undertaken in the hopes of understanding the true nature of being of which the Vedanta speaks. Karma Yoga is the path of action, ensuring that one's actions are reflective of good karma and in mirroring the actions in this life to the true and ultimate spirit that pervades all life. Bhakti Yoga is the path of devotion and identification with the higher plane of being to which one must strive. Jnana Yoga is the path of understanding that enables a cognitive frame of reference to embrace the true nature of reality. There has been a fourth Yoga added called Raja Yoga, which stresses the discipline of meditation as part of the acknowledgement experience. In accordance to the original question of "four levels," this could represent the four types of study that the Vedanta asks of us as we seek to better grasp the true nature of being in the world. However, I do not think that the study of Vedanta identifies four hierarchical levels simply because it would go against the notion of unity and symmetry that the Vedic texts all seem to articulate.