In general only non-linear instruments, like options, posses vega. Vega is always positive, no matter the directional component. So when you are long either a call or a put option you are long vega and when you are short either a call or a put option you are short vega.
Thereby it becomes clear that you can go long and short different option positions to offset vega. You cannot offset vega with linear instruments (underlying), i.e. stocks or indices (why? because their vega is zero!)
Two strategies come to mind: Risk-reversals and synthetics. A synthetic is a risk-reversal (simultaneous buying and selling of a call and a put) with the same strike which results in something similar to a futures contract. So basically by combining two non-linear instruments to replicate a linear one you eliminate vega.
See also this nice explanation: http://www.option-trading-guide.com/synthetics.html
Some general things to bear in mind:
- The more sources of risk you hedge away the fewer potential revenue streams remain. When you hedge all greeks you will loose the spread of all those positions -> so turning this around, this makes sense only for market-makers (and even they don't hedge all greeks completely).
- You still have to deal with model risk, e.g. when you use BS to calculate your hedges you will certainly be surprised by the outcome because of the non-normality of markets.
- Most hedges only work dynamically, i.e. when the market moves, you have to re-adjust which can be quite costly.
- Beware of ops-risk: You most certainly will not be able to establish all positions simultaneously with the limits you would like to have. Especially not in your example (high IV)!