Step 1: Recall the acidic versus basic trend.
Oxides of metals tend to be basic, while oxides of non-metals tend to be acidic. The more electropositive the metal, the more basic its oxide.
Step 2: Separate the given oxides.
The basic candidates are $\text{K}_2\text{O}$ and MgO (with $\text{Al}_2\text{O}_3$ amphoteric), while the acidic candidates are $\text{SO}_2$, $\text{P}_2\text{O}_5$, and $\text{SO}_3$.
Step 3: Pick the most basic.
Potassium is far more electropositive than magnesium, so $\text{K}_2\text{O}$ is the strongest base among them.
Step 4: Compare the acidic oxides by oxidation state.
Sulphur is $+6$ in $\text{SO}_3$ but only $+4$ in $\text{SO}_2$. A higher oxidation state makes the oxide more acidic, so $\text{SO}_3$ beats $\text{SO}_2$.
Step 5: Compare across elements.
Sulphur is more electronegative than phosphorus, so $\text{SO}_3$ is also more acidic than $\text{P}_2\text{O}_5$.
Step 6: State the pair.
The most acidic oxide is $\text{SO}_3$ and the most basic is $\text{K}_2\text{O}$, which is option 2.
\[ \boxed{\text{SO}_3,\ \text{K}_2\text{O}} \]