Wind elementals can be tough at a lower level, exactly because of that silence. In fact, they're possibly the toughest of all the elementals, outside Dark elementals. If you can silence them before they silence you, then you're set, otherwise you're toast. Other elementals will be easier for you, because they won't be using silence on you (silence is a wind-based spell)- for example, Earth elementals will use slow, and Water elementals poison.
As a BLM, your basic strategy is going to be to try to silence them right off the bat (doesn't always work with wind- as I mentioned, silence is aligned with wind, so they're highly resistant, and wind elementals love to spam blink too) and nuke with the element they're weak to. Having a staff instead of a wand may also help to do a bit more melee damage, but 95% of your damage will be from your spells.
As with everything else, it gets easier as you get higher. My husband sometimes hits an occasional wind elemental in La Thiene between ram hunting, and for him (level 52) he just uses one nuke (Blizzard 2), Aspirs to get his MP back, whacks it once with ice staff, and it's dead. He could farm forever like that, if there were just an unlimited supply of elementals, heh.
Keep in mind as you get up in level- the higher-level elementals have many nasty abilities that lower ones don't. For example, lightning elementals in Qufim always buff themselves with enthunder and shock spikes right after they spawn, and will use -ga spells and shock on you too.