Breaking apartment lease

Unfortunatey, the most we can tell you is "maybe." There is something called the "implied warranty of habitability"; this is an obligation, added by law to all leases, that the rental premises must be fit for inhabitation. If the landlord does not correct a condition affecting habitability after notice of it and a reasonable chance to do so, that continuing breach of the implied warranty of habitability can let the tenant terminate the lease without penalty.
The problem is, the test of when a condition is too bad to live with is essentially a subjective one, subject to personal opinion or interpretation: that is, if you break your lease and the landlord sues you for unpaid rent due under the lease, the matter will end up before a judge; the judge will listen to both sides and evaluate whether, in his/her opinion, the condition was so bad as to justify terminating the lease. A smell is not provable by hard evidence the way many other conditions are (for example: a mold condition or large leak can often be photographed); all you will have is your testimony, and against that, the landlord will put his (and maybe that of his super, a contractor, etc.) that he/they smelled little or nothing. So you are starting with a lack of evidence. And then, even if the judge believes you are smelling something foul and the landlord is not correcting it, this judge may or may not believe that a bad smell justifies moving out (i.e. the judge could believe it's just something you live with). So you could be found to have justification to mover out early--but you also might not be.