What's the quickest way to get rid of larvaes and [clothing] moths at home?
As a tenant I believe you've already done too much as this should be the land lords problem to rectify and not yours.

Notify the landlord verbally and in writing about the on going issue of the infestation in your apartment.

Contact your local city / town / government about your landlords responsibilities and your rights as a tenant in this type of a situation. Note: It may be possible to break the lease and move out without penalty should the landlord fail to rectify the situation in a certain amount of time.

If this was your dwelling: You've done everything you can and unfortunately the situation is beyond DIY and your control.

The best advise anyone can give is to contact an exterminator to have your hone sprayed. The problem with an infestation is that it needs to be addressed all at once, if you clear out one area and move onto another, it's possible that the moths to re-infest the original area and your at square one again. It only takes one for the cycle to start again.




  Local hardware shops have only cedar balls (new generation of moth-balls for clothes wardrobes) and spray cans that are useless for a deeper attack. Getting a pest consultant or whatever will NOT count as the desired answer, since I'm not a big fan of spending too much money on this.


Comment: In the case you have provided it is not for you the tenant to resolve. 

If this was a dwelling that you owned and you were responsible for you would still need to bring in a professional. The time and effort you've spend trying to eradicate this type of infestation (that has lasted weeks) by purchasing over the counter products and your time will be far more expensive than actually bringing in a professional.