Q: Texting apps that actually work for iOS 3.1.3?

A 3rd generation can be updated to iOS 5.1.1.

Connect your device to a Computer with iTunes installed and let iTunes search for an update.

With iOS 5.1.1 you will get a default Messages app by Apple (iMessage) will which let you text with other iPods, iPhones, iPads and Macs.

Are you sure it is a 3G? A

1G iPod can only go to iOS 3.1.3.

A 2G to 4.2.1 and

a 3G to 5.1.1

The 1G does NOT have volume buttons on the upper left edge

Identifying iPod models

I know of no texting apps for 3.1.3

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 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)       

https://buy.itunes.apple.com/WebObjects/MZFinance.woa/wa/touchLegacyLandingPage

A 2G to 4.2.1. Requires iTunes version 10.X. If a Mac it requires OSX 10.5.8 or later. With OSX 10.4.11 you can only go to iTunes 9.X which gets you as high as iOS 4.1

A 3G to 5.1.1  Requires iTunes version 10.5 or later

Since the iPod does not have a cellular radio, you need wifi for texting and all other apps that require an internet connection.