Can someone clarify landau symbols definition please?
In the case of $O(f(n))$ and $\Omega(f(n))$ you are correct in that they can be wildly inaccurate and still be correct, for instance, $n$ is $O(2^n)$ - this just does not provide good information.    

For $\Theta$ yes you can drop the lower orders of magnitude. What "$f(n)$ is $\Theta(g(n))$" means is that there are two constants, $C_1$ and $C_2$, and two values $n_1$, $n_2$ such that $C_1g(n)&gt;f(n)$ for all $n$ greater then $n_1$, and likewise $C_2g(n)Nf(n)$ for all $n$ greater then $n_2$. In your case we can see that multiplying $n^2$ even by 2 will dwarf the remaining values of $f(n)$ for sufficiently large $n$, likewise multiplying by 1 will make it always smaller.

Little $o$ and $\omega$ notation is used to describe a function as being orders of magnitude less then another. When we were in big $o$ notation, as long as one constant $C$ existed such that $Cg(n)&gt;f(n)$ then $f(n)$ is $O(g(n))$, with little $o$, every possible $c$ must cause this to happen. The easiest way to find this is to take the limit of $\lim_{x \to \infty} \frac{f(n)}{g(n)}$: if it is zero then $f(n)$ is $o(g(n))$; if it is $\infty$ then $f(n)$ is $\omega(g(n))$