Is it possible to transfer songs from my iPod to my iPhone?

I've tried pretty much everything. I've downloaded programs, made playlist, tried syncing it, and nothing seems to work. I think my iPod is the first generation and my iPhone is the 4s. I have about 200+ songs that I'd like to transfer. Help please?

Added (1). I'm on a shared computer so there are other songs that I don't want on itunes and not all of the songs on my iPod are on itunes.

The songs on your iPod are also available in iTunes on your computer?

iTunes is the way you transfer things between devices. Actually you use iTunes to transfer things to the devices, you can't transfer directly from iPod to iPhone.

Just plug in your iPhone and if the songs are purchased from the Apple account then log in. If not then just sync ONLY MUSIC with the iPhone. Remember only music! Then within the music app you can go to a song, slide to the left/right(forgot which side) but it can delete a song. Delete the ones you don't like so this way you don't have to mess up the shared computer library.

Surely you can transfer songs from your iPod to your iPhone without iTunes. Aiseesoft iPhone Transfer can transfer songs from one to another non-through iTunes.

You can use Syncios iPod Transfer to have a try.

That won't be a problem.
You can actually transfer your songs or anything else from your ipod to iphone/ipad as you like with the help of iphone/ipod/ipad to computer transfer if your apple products are on jailbroken condition.
First, you transfer your ipod music to itunes on your computer, then you can sync them to your iphone. It's that easy.
To help you clear the steps, here's a tutorial of how to transfer music from iPod to iTunes on PC: http://www.softwarebbs.com/wiki/How_to_transfer_music_from_iPod_to_iTunes_on_PC
Do as the tutorial and then sync the transfered songs from itunes ro iphone.

IPhone transfer may be the best choice. It supports Apple devices.