Do I need to know the curve for ECIES decryption? Let's assume that I have key pair generated using the following curves: brainpoolP256r1, brainpoolP320r1, brainpoolP384r1 or brainpoolP512r1.
Do I need information which curve was used to decrypt message? Can I infer which curve was used based on the private key?
This awfully looks like homework, but hey, here we go. Each curve has an order, which is the number of points on the curve (specifically, the number of points into a subgroup of prime order of the curve, but in the case of the Brainpool curves, the subgroup is the whole curve). A private key is a non-zero integer modulo the curve order; i.e. if the order is $n$, then the private key is a number between $1$ and $n-1$. In practice, the size of the private key, expressed in bits, will be close to the size of $n$ (the size in bits of an integer $x$ is the integer $k$ such that $2^{k-1} \leq x \lt 2^k$).

Curves brainpoolP256r1, brainpoolP320r1, brainpoolP384r1 and brainpoolP512r1 have orders of size 256, 320, 384 and 512 bits, respectively. Thus, look at the size of your private key; this should allow you to infer which curves you are talking about.

(Technically, a 255-bit integer, for instance, could be a valid private key for all four curves, since it would be in the accepted range for all four curves; however, probability that a private key, chosen uniformly in the range for brainpoolP320r1, ends up being a 255-bit integer, while it had a whole 320-bit range to chose from, is less than $2^{-35}$, so it won't happen often. In that sense, your answer won't be absolutely guaranteed to be correct in a mathematical sense, but it can be a good guess nonetheless.)