Q: how to reinstall apps on an old erased ipod?

You can redownload most iTunes purchases by:

Downloading past purchases from the App Store, iBookstore, and iTunes Store        

You will likel yhave to do the following for most apps

Starting when iOS 7 was released, Apple now allows downloading the last compatible version of some apps (iOS 4.2.1 and later only)

App Store: Downloading Older Versions of Apps on iOS - Apple Club

App Store: Install the latest compatible version of an app

You first have to download the non-compatible version on your computer. Then when you try to purchase the version on your iPod you will be offered a compatible version if one exists.

SInce you have iOS 4.1 ,your iPod can ve updated via iTunes to at least 4.2.1

To update

The Settings>General>Software Update comes with iOS 5 and later.

Connect the iPod to your computer and update via iTunes as far as your iPod model allows

iOS: How to update your iPhone, iPad, or iPod touch

- A 2G to 4.2.1. Requires iTunes version 10 or higher. If a Mac it requires OSX 10.5.8 or later.

- A 3G to 5.1.1  Requires iTunes version 10.5 or later

- A 4G (has cameras) to 6.1.6  Requires iTunes version 10.7 or later. For a Mac, that requires a Mac with OSX 10.6.8 or later

Identifying iPod models