Feel free to take the signs down. When walking through my neighborhood, if I see crap like this I just take them down and throw them out. You aren't breaking any laws tearing down those illegal signs. They are an eyesore!!

Are you sure that even though they are litter, in my opinion, they are of value and taking them would not be stealing?

No, you're not stealing something that is illegal. Now if they are on private property have have the permission of the property owner then yes it is stealing but if some clown is just putting up signs (especially on City/township property) then it is not stealing. If it is unlicensed litter as you say then it it can be collected and disposed of.