The legal clinic at U of C is Student Legal Assistance (403-220-6637).
Just like Calgary Legal Guidance, Student Legal Assistance is geared towards low income individuals. Before taking on your case, you will be grilled on your net worth down to car, bank accounts, assets of value. I forget what the threshold is...I seem to remember it being something like $24K.
While the reaction to sue the party with the deepest pockets is always most palatable...your remedies against the management company/landlord are likely limited. Check out the Residential Tenancies Act and the terms of your lease. It seems like your lease was frustrated (no longer in a condition that could be lived in). It also sounds like your lease had a termination clause applicable to the frustrating circumstances which kicked in. Bottom line, big picture - in a frustrated contract the parties are freed from their obligations. The tenant is entitled to recover monies paid for the lease for which the tenant did not get to enjoy (ex. you paid the month's rent but only occupied premises for 15 days). In a terminated contract - parties walk away from the contract in accordance with the termination provisions of the lease. Sure...you can argue the landlord/management company had a duty of care to you which it failed to meet and seek damages. However, as other posters have commented...it all turns on facts...landlord will argue that the other tenant was the cause of your damages.
As for going against the other tenant - you are going to be alleging that the tenant was negligent (a tort - a civil wrong doing). Read up on the law of negligence and consider the law of nuisance as well (although the ability to argue nuisance really turns on facts). There are lots of online resources that explain direct and consequential damages in tort matters. Your success in obtaining things like lost wages, etc. will turn on the foreseeability of those damages.
Small claims court is truly the people's court. The judge is not going to expect lay people nor does the system require people to argue legal principles as if they were appearing before a judge at Queen's Bench. First, familiarize yourself with the legal principles. Prepare a detailed statement of facts along with all supporting documentation. Be prepared to connect the dots in how your facts relate to the legal principles.
As other posters have commented - success in small claims court is not difficult. It's the enforecement of a judgement that can be very difficult depending on the circumstances.