1. How and where to include JavaScript Files in Angular Project?

You need to include your JS file in the asset folder and refer this JS file in .angular-cli.json file.

Refer the snapshot's,

Folder structure should be like this.

.angular-cli.json

2. How to call the JavaScript Functions from Typescript class?

your TS should be like this.

myJsFile.js file content.

This sample logic mentioned above will work, I have tried and tested using version 4, So I am expecting it to work with version 5 also.

Updating the answer for the new Angular version release. Working perfectly till version 11.2.6.

Find the code (function with parameter) here for Angular11

The given answer by Arun Raj R is perfect.

But for the angular 6+ project you need to take angular.json instead of angular-cli.json.

also if you want to pass parameter inside external function that come from js file than use just function name.

For Ex :

app.component.ts

import { Component, OnInit, ViewChild, ElementRef } from '@angular/core';
declare function myfunction: any; // just change here from arun answer.

@Component({
  selector: 'app-test',
  templateUrl: './test.component.html',
  styleUrls: ['./test.component.scss']
})
export class TestComponent implements OnInit {
    constructor() { }

    ngOnInit() { 
        myfunction('test1', 'test2');
    }
};

yourJs file :

function myfunction(params1, params2) {
    console.log('param1', params1);
    console.log('param2', params2);
}