Is is possible to add NO2X, AlX3 to achieve nitration of benzene?
Nitration using nitryl chloride($\ce{NO2Cl}$) was studied extensively by Price and Sears where they found $\ce{AlCl3}$ to be a suitable reagent for the reaction. They also noted that nitration was difficult for deactivating aromatics such as halobenzene and benzotrifluoride and hence this method was considered of limited value.
On further experimentation, it was found that $\ce{TiCl4}$ was the best suitable catalyst. Other reagents used were $\ce{FeCl3,ZrCl4,AlCl3}$ and $\ce{AlBr3}$ but the reaction conditions were difficult to control. $\ce{BCl3}$ gave smaller yield with possible ring chlorination and $\ce{SbCl5}$ were effective for only aromatic compounds. The following compounds were nitrated using nitryl chloride and $\ce{TiCl4}$ as catalyst and data was noted:
\begin{array}{c|c}
\mathbf{Compound} &amp; \mathbf{Yield (percent)} \\\hline
\text{benzene} &amp; \text{88%}\\
\text{toluene} &amp; \text{81.5%} \\
\text{ethylbenzene} &amp; \text{79%}\\
\text{fluorobenzene} &amp; \text{91%}\\
\text{chlorobenzene} &amp; \text{89%}\\
\text{bromobenzene} &amp; \text{86.5%}\\
\text{o-dichlorobenzene} &amp; \text{41.5%}\\
\text{benzotrifluoride} &amp; \text{32%}\end{array}
An excess of solvent was used for the reaction. Tetramethyl sulfone was suitable for the reaction. Other solvent experimented with was carbon tetrachloride but many chlorinated byproducts were observed. The possible mechanism for the reaction (with $\ce{AlCl3}$ as catalyst) was noted:

or a possible salt formation mechanism was indicated:
$$\ce{NOCl2 + AlCl3 &lt;=&gt; NO2+AlCl4-}$$
Nitration using Nitryl chloride was once important in making chloronitrosoalkane where carbon-carbon double/triple bond were broken by nitryl chloride and an free radical addition reaction occured but the yield was not that high. Dinitromethane was used as solvent as nitryl chloride breaked into chlorine and nitrous oxide:
$$\ce{NO2Cl -&gt; NO2 + Cl.}$$
$$\ce{CH2=CH2 -&gt;[NO2Cl] Cl-CH2-CH2-NO2(45 {%}) + Cl-CH2-CH2-ONO(35 {%}) + CH2Cl2 + N2O4}$$
$$\ce{C2H5-C#C-C2H5 + NO2Cl -&gt; C2H5-ClC=CNO2-C2H5}$$
As for nitryl bromide, it was found to be unstable. Zuskin et. al. claimed to have synthesized the product$\ce{^{[4]}}$ but were invalidated due to their instability. Many attempts$\ce{^{[5]}}$ of making nitryl bromide were made but failed as they decomposed to nitric oxide and bromine. So, nitryl bromide was observed as a combined entity of (nitryl chloride + $\ce{KBr}$ in sulfur dioxide) at $\pu{-20 ^{\circ}C}$ and using $\ce{TiBr4}$ as catalyst, nitration was done but yields were low(lower than that observed with nitryl chloride) with possible ring-brominated side products. This is due to interference of side products from partly decomposed nitryl bromide.
Notes and References

Across Conventional Lines: Selected Papers by George A Olah, G K Surya Prakash

Chemistry of Energetic Materials by George A. Olah, David R. Squire

Nitrate Esters Chemistry and Technology by Jiping Liu

Bromine vapor saturated with nitrogen peroxide passed through a tube filled with bone-ash at $\pu{200-250^{\circ}C}$.

Halogen exchange of nitryl chloride with $\ce{KBr}$ in liquid $\ce{SO2}$, reaction of $\ce{BBr3}$ with anhydrous niyric acid or dinitrgen pentoxide, reaction of bromosulfonic acid with nitric acid and ozonolysis of nitrosyl bromide.