the strongest army is, ofcourse, broodlord/infestor/queen/ultralisk.
kind of expensive.
in an actual game scenario, they will usually push with hellion/banshee, so teching up to mutas very quickly is usually your best option. try to kill off the hellions and banshees before taking too much eco damage and then use your mutas to take full map control, delay his third, and force turrets if possible.
at this point he starts producing thors 2 at a time, and depending on the game, you have a decision to make. either go roach/ling allin (u can use drop here if u like) or tech up to tier 3. if u are going for tier3, get 10 infestors so they start banking energy, and if he pushes before u can get to tier 3, u hold down the r button and overrun him with roach/infestor/ling.
queens are great for antiair and transfuse, they can keep your broodlords alive a LONG time and kill off those last 2-3 vikings.
NP is also very good. u can either NP thors if he only has a few left or 1 is out of position, or u can NP vikings and make them shoot at the other vikings, then land them, which effectively kills them.
otherwise u get yourself a nice little deathball of queens, infestors, and broodlords. ultras are optional, but they are good to close the gap to broodlords since he will likely be going for some push to hit before broods are out, so thats why i usually get them, unless he already did a fail allin that i held with roach.