Is it possible for halogens to show oxidation states less than -1?
Yes, they can show oxidation states lower than -1. For example in hyperlithiated compounds, like $\ce{Li3Cl}$, the chlorine would formally have an oxidation state of -3.

However, a word of caution, oxidation states are a tricky thing. They are determined by adopting the hypothetical view that the compound you are looking at consists only of single-atomic ions, e.g. in the case of $\ce{Li3Cl}$ of 3 $\ce{Li+}$ and $\ce{Cl^{3-}}$. The hypothetical charges of these "ions" are then your oxidation states. Clearly, this view has nothing to do with the real bonding situation in the compound and oxidation numbers correlate very poorly with the real electron distribution. It is simply a useful little device for keeping track of redox reactions. So, the -3 oxidation state of chlorine in $\ce{Li3Cl}$ does not mean that chlorine has a 10-electron valence shell. The real bonding situation will be somewhat more complicated.