The elliptic algebra $A_{q,p}(sl(N)_{c})$ at the critical level $c=-N$ has an extended center containing trace-like operators $t(z)$. Families of Poisson structures, defining q-deformations of the $W_N$ algebra, are constructed. The operators $t(z)$ also close an exchange algebra when $(-p^{1/2})^{NM} = q^{-c-N}$ for $M \in Z$. It becomes Abelian when in addition $p=q^{Nh}$ where $h$ is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed $W_N$ algebras depending on the parity of $h$, characterizing the exchange structures at $p =/ q^{Nh}$ as new $W_{q,p}(sl(N))$ algebras.