It's not very hard.
Strength of a gorilla obviously possible, since gorillas have it. Eight feet tall perhaps possible, but this would be hard for upright position - can they also have posture akin to that of gorillas?
Immune to aging is probably very easy as soon as we figure out how aging works. They have to die eventually, but it's possible that they are very long-lived and with very sudden onset of disability and death (they live to the full then drop dead).
Immune to disease is not hard to engineer: we could modify their biochemistry to be incompatible with most of earth biome (change how some amino acids are coded, change some organic molecules left to right) so that most bacteria and all viruses won't thrive. Of course, they are vulnerable to specifically crafted modified diseases, that's their Achilles' heel.
It's harder to make them immune to autosomal diseases. I guess some of these will still manifest. However, you can handwave that they're pretty rare and usually detected in early life & removed from population.
Resistance to radiation is probably not very hard either - many organisms do that, we even know how they do it. Please note that radiation is exponential phenomenon - we can make them perform indefinitely in "not great, not terrible" environment, but they definitely won't withstand naked reactor core.