Convert three functions into a single function
I think your code would be cleanest if you wrote the program as a composition of a minimum-absolute-value-of-array function and a filter.

Assuming that performance in the face of large data sets is not a concern, you could have, for example:

function isNumber(val) {
    return typeof val == "number";
}

getClosestToZero(myNumbersToSort.filter(isNumber));


Alternatively, getClosestToZero() could directly support an optional second argument that servers as a filtering callback if it is provided.

Please pay attention to the consistency of the indentation.