Okay, if I'm taking this the right way, we (very simply) think about it this way, sp hybridised as a triple bond (i.e multiple bond to the other heteroatom in the case of nitrogen, carbon is a triple bond and a single bond to a hydrogen). sp2 hydridised is a multiple bond and single bonds, and sp3 hybridised is single bonds.
I realise that makes little sense tbh.
So yes, N2 is sp hybridised, and is linear.
N2H2 (which I'm pretty sure doesn't exist, tbh) has a double bond between the nitrogen atoms, and a single bond to each hydrogen, making is sp2, I think. I'm pretty sure it would not be linear, because the lone pairs lie "next" to one another rather than opposite one another.
N2H4 has just single bonds, making it sp3 hybridised.
I always think about it more about the bonds, rather than the shape of the molecule. But then again we've only talked about hybridisation in relation to carbon.
Of course, hybridisation is another of those lies that they tell you.
N2H2 may exist (probably only transiently, though) - it might be one of the intermediates in the reduction of nitrogen to ammonia by dinitrogenase enzymes (generally iron- or molybdenum- containing, these metal ions being electron donors in the reductive process) in species such as Azotobacter.
I would also agree with PoisonDonna on its geometry - it would be similar to that of hydrogen peroxide, just with one repulsive LP instead of two.
Let's get this clear: everything hybridises (with the possible exception of hydrogen), because hybridisation is just a way of explaining the shapes of molecular orbitals as if they were made from atomic orbitals.
However, atoms and molecules are two completely different types of species. Atoms only have one nuclear centre and so form atomic orbitals with atomic shapes, whereas molecules have multiple nuclear centres and form molecular shaped orbitals. All hybridisation tries to do is explain a process that actually almost never occurs, i.e. how to form molecules from atoms.
In reality moledules are virtually never formed from atoms except in extreme cases such as cooling a vapour from thousands of degrees.
So the process is hypothetical. The question is really asking how do we explain that atoms have orbitals of one shape and molecules orbitals of another?
What we actually need to recognise is how to answer the question of the type of hybridisation present (assuming the process of hybridisation):
1. If an atom has all single bonds and an octet of electrons then it is sp3 (electronically tetrahedral)
2. If an atom has one double bond and an octet of electrons then it is sp2 (electronically trigonal planar)
3. If an atom has either two double bonds, or one triple bond and an octet of electrons it is sp (linear).
Electron deficient centres (eg NO2), just treat the lone electron as if it were a pair for the hybridisation and the geometry and use the rules above.
Molecules that have expanded octets such as PCl5 use different hybridisations like sp3d, however these are not difficult to learn as there are so few of them.
u know smth our chem teacher told us that we need 2 just briefly know abt hybridisation...cuz all those details rarely appear in xam papers!
The reason why N2H4 is sp3 is because it is made up of four electron domains and the reason for that is because the lone pairs on each Nitrogen atom are included when deducing its hybridization.