Why is acetic acid stronger than p-nitrophenol?
The difference in acidity between acetic acid and phenol can be attributed to the electron-withdrawing properties of a carbonyl function versus a phenyl ring. In both cases, the deprotonated oxygen can be depicted in a resonance structure as forming a double bond to the carbon in question and the charge being delocalised within the ring.

It should immediately strike anybody that a phenyl ring primarily provides a resonance body (i.e. a greater volume into which the charge can be delocalised) while a carbonyl group is also actively withdrawing (both inductively and mesomericly). This is reflected when comparing the $\mathrm{p}K_\mathrm{a}$ values of $\ce{CH3CO-CH3}$ (acetone) and $\ce{Ph-CH3}$ (toluene) — $16.5$ logarithmic units in $\mathrm{DMSO}$ according to the Evans table[1] or approximately $24$ logarithmic units in water ($\mathrm{p}K_\mathrm{a}$ of acetone in water taken from the Brodwell data).[2]

Adding a nitro group to the phenyl ring reduces this difference drastically to $-6.1$ logarithmic units (i.e. para-nitrotoluene is more acidic than acetic acid) — in $\ce{DMSO}$. One should always remember that acidity differences in one solvent can be drastically different in another solvent. For example, the difference between $\ce{MsOH}$ and $\ce{TfOH}$ is $11.4$ logarithmic units in water but only $1.3$ logarthmic units in $\ce{DMSO}$ (that is not a typo). One should also note the difference between acetic acid in water ($\mathrm{p}K_\mathrm{a}\approx4.76$) and $\ce{DMSO}$ ($\mathrm{p}K_\mathrm{a}\approx12.3$).

$$\textbf{Table 1: }\text{Acidity constants of various compounds in various media}\\\text{All data taken from the Evans data unless noted otherwise in the text.}$$
\begin{array}{lrc}\hline
\text{compound} &amp; \mathrm{p}K_\mathrm{a}(\ce{H2O}) &amp; \mathrm{p}K_\mathrm{a}(\ce{DMSO})\\ \hline
\ce{CH3CO-CH3} &amp; 19.3\phantom{000} &amp; 26.5\\
\ce{Ph-CH3} &amp; 31.5\phantom{000} &amp; 30.6\\
\ce{$p${-}NO2-C6H4-CH3} &amp; &amp; 20.4\\
\ce{MsOH} &amp; -2.6\phantom{000} &amp; \phantom{0}1.6 \\
\ce{TsOH} &amp; -14\phantom{.0000} &amp; \phantom{0}0.3 \\
\ce{AcOH} &amp; 4.76\phantom{00} &amp; 12.3\\ \hline \end{array}

Given that a $\mathrm{p}K_\mathrm{a}$ value of para-nitrotoluene has not been reported in water (although it’s $\mathrm{p}K_\mathrm{b}$ value has been),[3] we are not in any position to draw definite conclusions. However, water being the solvent it is, I would still assume the electron-withdrawing ability of a nitro group which relies solely on mesomeric effects to be weaker than the effect of a directly neighbouring carbonyl group. Remember that water is excellent at stabilising charges; $\ce{DMSO}$ not so much.



References:

[1]: The Evans $\mathrm{p}K_\mathrm{a}$ table

[2]: The Brodwell $\mathrm{p}K_\mathrm{a}$ data

[3]: J. C. D. Brand, J. Chem. Soc. 1950, 997. DOI: 10.1039/JR9500000997.