For finding the outliers, Do we need to normalize the Data?
this is certainly recommended, yes. All outlier detection methods depend on distances and / or densities and distance calculations can be really skewed on non-normalized data.
Can you please tell me impact without normalizing?
If you have a single dimension with a much larger scale than the other dimensions, this single dimension might overrule the others.
Which methods are best for Normalized data for Outlier detection?
Totally depends, there should probably also be a No-Free-Lunch-Theorem for outlier detection
In general, I have good experiences with the local outlier factor method.
And Which methods are better if I don't want to normalize?
Don't do this (see above).