What is the chemical structure / hybridization of sulfuric acid?
It is much easier to explain it on simpler example – $\ce{O3}$ molecule. It has structure of resonance hybrid of $\ce{O=O+-O-}$ and its mirror. And of course, central atom has hybridization state $sp^2$. One bond here is normal covalent bond and another bond is dative: an electron pair is donated onto vacant orbital of $\ce{O}$ atom with all electrons paired. in $\ce{H2SO4}$ molecule to bonds are simple covalent ($\ce{S-OH}$ ones) and two are dative ($\ce{S-O}$ ones). A common concept of electron unpairing to my knowledge is proved brocken by quantum chemistry calculations and spectral experiments for hypervalent compounds of $\ce{P}$ and $\ce{S}$.

A little more interesting example is $\ce{XeF2}$ molecule, where three-atom four-electron bond $\ce{F-Xe-F}$ are formed, that can be think of as reasonance hybrid of structure $\ce{F-Xe+\ F-}$ and its mirror $\ce{F- \ Xe+-F}$ 

Of course, this scheme is still far from perfect, as reality is much more complicated, but if you do not wish to take course of quantum chemistry, it should be enough. However, I'll recommend to search for "MO LCAO model": it is quite simple and very useful. It is also often used in advanced chemistry books and articles.