I tend not to pay attention to type strengths/weaknesses, most of the time you can work around these with proper switching.
For my battles, I favor party-enhancing moves such as Agility or Swords Dance. After all, if you use Growl or Leer, it works only on the current foe, and once you faint it you'll have to start all over again with the next foe. In my master team, Scyther has both moves, combine with Slash and HyperBeam.
If my party is too underleveled to have such attack, or straighty won't learn them, I work my way with moves that have a prolonged effect. Supersonic/Confuse Ray and anything that can inflict Paralysis are my favourites, and then my life saver, my trusty starter Ivysaur's Leech Seed. I can't emphatize enough the way that move has saved me from rough spots, including surpresively unprepared Rival fights. I don't use Toxic because I somehow forgot it existed. But I'll work around that soon...
Oh, and there is always a Pokémon in my team that has a surprise move, like Horn Drill or Flail, coupled with a multihit like Doubleslap... Just in case I have time to do some DireHit or X-Attack...