Option #1 sound more natural to my (American layman) ear:
"They help in carrying oxygen to the body's cells."
But this choice is very context related.
If you are emphasizing the distinction between one kind of cell and all other cells, laymen would usually say "body cells". People in the medical profession would usually say "somatic cells", unless they are talking to laymen. For example, "somatic cells" can mean "non-nerve cells", "diploid cells" (as opposed to "haploid cells", or "non-germ-line cells".
The word "somatic" is not natural. Of the people who use it, most were required to consciously learn (or memorize) it as an adult. Ironically, many food marketers use the word "somatic" to imply that a product is "natural".
"Layman" means an ordinary person, as opposed to someone who has been trained in <a learned profession>. In this explanation, "layman" = "someone who is not in the medical profession". The original example was "layman" = "someone who is not a nun, priest, or other member of the clergy". In other contexts, the <learned profession> might be magic, or law, or science.