The C-13 chemical shift of acyl chlorides vs ketones In lectures, we were taught that ketones and aldehydes tend to have chemical shifts of around 200ppm, while acid derivatives (carboxylic acids esters etc) tend to have values around 160-170 ppm.

The reasoning given by my supervisor was that despite acid derivatives having more electron withdrawing groups, due to conjugation, the net effect was that these additional groups donated electron density to the carbonyl carbon, hence shielding it more than the carbonyl carbons in ketones/aldehydes (i.e. the conjugative effect dominates over the inductive effect). This all makes sense for me except for acyl chlorides.

The reason why acyl chlorides are not adding up for me is that in the very next topic, we were taught that the CO double bond of an acyl chloride is stronger than that of a ketone/aldehyde! Since carbonyl bonds are strengthened by anything that withdraws electrons, I can only conclude that the Cl has a net electron withdrawing effect (i.e. its inductive effect dominates the conjugative effect).

Since the Cl group appears to actually withdraw electron density, going back to NMR, shouldn't the carbonyl carbon in acyl chlorides resonate at a higher frequency than the carbonyl carbon in a ketone/aldehyde?
Halogens $(\ce{Cl},$ $\ce{Br},$ $\ce{I})$ also act as conjugative donors. Not very good ones but you still have to take that into account especially because, as you said, conjugative effect is larger than inductive effect (and it is very different in $\ce{^1H}$- or $\ce{^13C}$-NMR).
The $\ce{^13C}$ chemical shift in $\ce{CH2Cl2}$ is $\pu{53 ppm}$ but the one for $\ce{CH2I2}$ is $\pu{–62 ppm}$ (yes, with a minus sign).