The natural-sounding ones are 1) 「空腹の野生の猫」and 3) 「空腹の野生猫」. Between those two, 3) sounds slighly more "formal" than 1) for not using 「の」 repeatedly, but both are equally correct.
2) 「空腹野生の猫」 would have to be called "very awkward" and also "incorrect" because the double compound 「空腹野生」 is not at all common; therefore, our eyes and ears are not ready to take it in without feeling an amount of stress.
Multiple-compound kanji terms need to be either already fairly common or easily predictable for the native speakers to feel comfortable with them. That is why a very long one such as 「早稲田大学文学部入学試験会場入口」 looks and sounds completely natural and "correct" while a much shorter 「空腹野生」 looks problematic.
Finally, 4) 「空腹野生猫」 is simply out of the question. You might find it in creative writing, where basically everything is "correct" in the first place, you would not use it in a composition or academic paper.
Every native speaker would certainly understand what is meant by 「空腹野生猫」 if you said/wrote it, but it is just not something they would say or write in a natural setting.