If it is a single and unique dataset you may apply first a translation by adding 1 and subtracting the minimum T= X+1-min(X) and then log, but if you want it to apply to any dataset the min() should be the absolute one. For scientiphic consensus please follow specific literature refs.
Thank you Sir Bongi. I have done that way only. The transformation techniques i have employed are viz., Square, Log, Reflect and Sqrt, Reflect and Log and reciprocal for the data set with negative values. Could you please guide me some more.
One assumption for doing ANOVA is having data with normal distribution. Since your data doesn't follow it as you said, it is not recommended ANOVA but non-parametric analysis. However, you could try to "normalize" your data and check if you succeeded. I suggest you to seek help from a statistician nearby.