sketching magnitude of frequency response of H(z)
Since you have the transfer function factored into poles and zeros, it's easiest to draw the pole-zero diagram to get an idea of the overall shape of $H(z)$. The first thing you notice is the pole at $z=1$, i.e. at DC. So your filter is unstable and $|H(e^{j\omega})|$ goes to infinity at DC. Furthermore there's a complex conjugate pole pair on the imaginary axis, i.e. at half the Nyquist frequency. So you can expect a small bump around that frequency. Finally, I would calculate the value of $H(z)$ at Nyquist, i.e. at $z=-1$:

$$H(-1)=\frac{3\cdot 0.5\cdot 0.1}{2\cdot 1.49}\approx 0.05$$

A more detailed sketch than that is indeed difficult, but that's probably not the idea of the exercise.