今は休暇だから本を読んでるし、泳げるようになってるし、リラックスしてる。
This is just my opinion for this particular sentence, but I'd go with the ～たり form here:
今は休暇だから本を読んでたり、泳げるようになってたり、リラックスしてる。
～し lists either actions or qualities, and while it resembles ～たり in that it doesn't specify an order in which the actions took place, it adds a "not only, but also" implication to it:
今年の夏は海に行ったし、山にも行った。 This summer I went to the ocean, and [not only that, I also went] to the mountains.
荷物が多いし、雨も降ってきたし、どこかで休もうか。 We've a lot of luggage, and [not only this, but] it's started to rain, so shall we take a break somewhere?
(Above examples taken from page 198 of 初級を教える人のための日本語文法ハンドブック)
In sentences like the second one above, where multiple ～し constructions are used to provide reasons, as you saw in the other question, the last し can be replaced with から with hardly any change in meaning:
荷物が多いし、雨も降ってきたから、どこかで休もうか。 We've a lot of luggage, and it's started to rain, so shall we take a break somewhere?
～し can also get tacked onto the end of a sentence when that sentence provides justification for an immediately preceding statement:
せっかくパリまで来たんだから、観光でもしよう。天気もいいし。 We've come all the way to Paris, so let's do some sightseeing. The weather's nice, too.
このお店はすごくおいしいですよ。かなり安いですし。 The food here is amazingly good. And it's easy on the wallet, too.
～し can be used in both informal and formal settings (as seen in the second example immediately above, it can follow the polite form).
Mark Hosang kindly pointed out in the comments that in formal speech (and perhaps most commonly in written Japanese), the ～ます stem form of the verb する (し) is used as a transition between clauses, just as the ～て form (して) is used in spoken Japanese. From ALC:
上海の不動産価格は去年1年間で24％増加し、今では中国で1番高くなっています。
Shanghai's real estate prices increased 24 percent over last year, and are now the highest in the country.
This is unrelated to the ～し form discussed in this question.
