The correct order of the basic strength of following compounds is

Due to the presence of lone pairs of electrons on nitrogen atoms, amides are known to be basic in nature. And their strong tendency of donating electrons demonstrates their basic strength. 

•  compound 1 is an aliphatic amine and the rest are aromatic/aryl amines. 
• Aliphatic amines are more basic than aromatic amines because, in aromatic amines, the delocalization of electrons takes place thus increasing their stability. So, fewer electrons are available for donation. Hence, compound 1 comes first.
• The $-{\mathrm{CH}}_3$ group attached to aniline increases its basic strength because the $-{\mathrm{CH}}_3$ group is an electron donating group so, more electron density hence, more donating ability. So, compound 3 has more basic strength than compound 1.
• The –CN group is an electron-withdrawing group, hence it destabilizes the ring. And so has the least basic strength among all.

Thus, the correct order of basic strength of the compounds is 1 > 3 > 2 > 4.

Therefore, option (C) is correct.