I would take the vent louvers out of the dash; If they are like the LR4 they simply pull straight off, then set the air distribution to blow from the front facing vents, then get a powerful shop vac insert the pipe into the vent and block each successive vent while letting the vac do its job, this forces it to suck through each pipe in turn.
Also, remove the cabin air filter and vacuum up inside the housing to clean it out. When you are done, put the shop vac back on the vents (with others blocked in turn) spray Lysol up inside the cabin air filter housing while the vac sucks air through. Do each vent in turn. This should help to knock out any smells.
If your heater blows cold, check your coolant level. If you can feel the heater getting hot under the dash board, your air distribution flap may be blocked or broken (by the rodent nest perhaps?)
This may take several goes to clear out the crap, just work through it logically.