what is mesomericeffect andorders of stability regarding this effect

Aromaticity > Resonance > Mesomeric > Inductive.

Reason:

Aromaticityis explained by Huckel’s Rule

the molecule must follow Hückel's rule, having 4n+ 2 electrons in the delocalized, conjugated p-orbital cloud;
the molecule must be able to be planar;
the molecule must be cyclic; and,
every atom in the ring must be able to participate in delocalizing the electrons by having a p-orbital or an unshared pair of electrons.

All the above terms finally account for highest electron delocalization means higher stability.

Resonanceis also explained by delocalization of electrons and also the development of partial negative or positive charge on an atom which it can withstand.

Mesomeric Effectis negative (–M) when a substituent is an electron-withdrawing group and the effect is positive (+M) when based on resonance and the substituent is an electron releasing group.

Inductive effectis considered weak as it effect almost gets vanished after 2 bond distance.