Eliminating elements in a javascript array

Should I use typeof?

Yes, you should and chain the conditions with logical AND while testing for unequalness.

var array = [NaN, 0, '0', undefined, null, false];

array = array.filter(function (a) {
    return typeof a !== 'string' && typeof a !== 'boolean';
});

console.log(array);

You can use typeof operator in filter() method callback, eg:

const myArray = [1,'foo',{name:'bar'},true];
myArray.filter(e => typeof e !== 'string' && typeof e !== 'boolean');

If you use this sort of filtering a lot, you can create a generic type filtering method. The method will receive as params, isType methods for types that will be filtered out.

const array = [NaN, 0, 'string', undefined, null, false];

const isType = (type) => (v) => typeof v === type; // generic type method using partial application
const isString = isType('string'); // detects strings
const isBoolean = isType('boolean'); // detects booleans

const filterTypes = (arr, ...typesToFilter) => 
  arr.filter((v) => !typesToFilter.some((isType) => isType(v))); // remove all items that are of one of the typesToFilter

const result = filterTypes(array, isString, isBoolean);

console.log(result);

You can do it that way using typeof and array.filter() function

    var getNone = x => typeof x !== 'string' && typeof x !=='boolean'; 
    var arr = ['henry',true,1,0,5,'charles',false].filter(getNone);
    console.log(arr);