Alternately means switching between two alternatives, alternatively means doing something different.
I love pizza and Mexican food, I eat them alternately.
Means Monday I ate pizza, Tuesday tacos, Wednesday pizza again, Thursday burrito, Friday went to the Hospital to get my arteries roto-rooted.
I love pizza but alternatively I eat Mexican.
Means both choices are good, but says nothing about when or the order in which I eat them.
Alternately is about switching. Alternatively is about enumerating options.
With means 'accompanied' or 'by'.
In means 'enclosed' or 'surrounded by'.
Method overloading is calling what appears to be the same function in a program but - because different arguments can be given to the function - it is technically a different method being called. This concept of multiple methods that are the same is known as method overloading.
Varargs is shorthand for 'variable arguments' and is a way of passing a set of arguments to a method without explicitly identifying each individual argument.
Putting it all together:
1) Method overloading can be performed by (using) varargs. So 'method overloading with varargs' is fine.
2) Varargs and method overloading as programming concepts accompany each other. You use different arguments for the same named function in overloading. You provide different arguments to a method with varargs. So 'varargs with method overloading' also works.
3) Method overloading does not need to involve varargs. You can overload a method that takes only one argument instead of a set for instance. These other implementations suggest that conceptually method overloading is larger than, and encompasses, varargs. So 'varargs in method overloading' is correct.
You should not say method overloading in varargs. They can't enclose each other.
I would suggest that all three of the above are perfectly valid. Of them perhaps 2) would generally be less used, but in the context of your question, is absolutely correct.
Best Answer
It really depends on the circumstances that you find both in. In each case adding "The" to the front of the line would improve it, and the bottom line is certainly the easiest on the ears and rolls off the tongue. However, as I assume this is being used with regards computing, the top line is shorter and does give the same impression to the computer savvy.