Key Size for Symmetric Homomorphic Encryption Over the Integers
The paper says that the parameters are $r ≈ 2^{\sqrt \eta}$ and $q ≈ 2^{\eta^3}$. Note that these values are expressed as functions of $\eta$,  not $N$. 

With regard to the parameters, it is common practice to describe them using the asymptotic notation. $\omega(\cdot), \Theta(\cdot)$ and $\tilde O(\cdot)$ are instances of this notation. $\omega(g(n))$ denotes a function that dominates $g(n)$ asymptotically; that is, $f(n) = \omega(g(n))$ means that $f(n)$ is asymptotically greater than $g(n)$. For example, a linear function (e.g., $f(n) = n$) dominates a logarithmic function (e.g., $g(n) = \log n$), since, asymptotically, it grows much faster; thus, $n = \omega (\log n)$. $\Theta(g(n))$ denotes a function that, also asymptotically, can be "sandwiched" between $k_0 \cdot g(n)$ and $k_1 \cdot g(n)$, for some real values $k_0, k_1 &gt; 0$. Finally, $\tilde O(n)$ is like the traditional Big-O notation but ignoring any logarithmic factors.

Therefore, these parameters are actually functions of the parameter $\lambda$, since they vary when $\lambda$ varies, although they are not expressed as functions. The expressions given are only a way of specifying how to choose them according to $\lambda$.

Also note that these expressions are somewhat "abusing the notation", since these asymptotic "functions" are actually sets of functions. Therefore, when you see something like $\rho = \omega(\log \lambda)$, it actually means $\rho(\lambda) \in \omega(\log \lambda)$. Anyway, this is a fairly common convention that simplifies the reading.

Knowing this, you can deduce your own example values for the parameters. For example:

$$\rho = \omega(\log \lambda) \to \rho =  \lambda$$
$$\eta \geq \rho \cdot \Theta(\lambda\log^2 \lambda) \to \eta = \lambda \cdot (\lambda\log^2 \lambda) = \lambda^2\log^2 \lambda $$
$$\gamma = \omega(\eta^2\log \lambda) \to \gamma = \eta^2\lambda = (\lambda^2\log^2 \lambda)^2\lambda = \lambda^5\log^4 \lambda$$
$$\tau \geq \gamma + \omega(\log \lambda) \to \tau = \gamma + \lambda = \lambda^5\log^4 \lambda +\lambda $$
$$\rho' = \rho + \omega(\log \lambda) \to \rho' = \rho + \lambda = 2\lambda$$

As you can see, this gives a result that is consistent with the part that says:


  A convenient parameter set to keep in mind is $ρ = λ$, $ρ′ = 2λ$, $η = \tilde O(λ^2)$, $γ = \tilde O(λ^5)$ and $τ = γ + λ$. (This setting results in a scheme
  with complexity $\tilde O(λ^{10})$.)


When it says that the scheme has complexity $O(\lambda^{10})$, I guess it means the time complexity.