When using あまり and そんなに with a verb, for example: そんなにいらない and あまりいらない, is there a difference? I think they both translate to "I don't really need it"
Yes, there are subtle differences.
With そんなにいらない, you should mentally picture a pile, and you are pointing at it and saying "I don't need that much" or "I need less than that" but you still need it to some extent, just not as much as that. With あまりいらない, there's no subject of the comparison. You are just saying your need is small to non-existent.
On the spectrum of "I need it badly" to "I definitely don't want it," when I hear "I don't really need it" it's pretty firmly on the negative side. そんなにいらない can be used in that situation, but it's also often used when you do need it. Consider this:
塩は大さじ一杯くらい？ (would one table spoon worth of salt do?)
あー、そんなにいらない！小さじ一杯くらいで十分。 (That's way too much. One tea spoon would be plenty)