"I hate running."
As far as I understand の is used as a nominizing suffix here. It changes the phrase (verb) "to run" into something like a noun: "the action of running"
Yep. の normalises a verb into a noun. For English speakers, it makes run into running. You wouldn't say "I hate run" but you would say "I hate running"
きらい doesn't mean hate, rather it means dislike. Hate would actually be だいきらい
Short answer: yes, it's possible.
Long answer: there are many rules surrounding nominalizers こと and の.
の is used when nominalizing clauses dealing with immediate time and/or location. In these cases, only の is allowed:
1) When clauses deal with senses: 誰かが叫ぶのが聞こえた。
2) When second clause occurs at the same time as the first one: これを運ぶのを手伝ってください。
3) When the second clause has a verb dealing with stopping of cancellation of something: お酒を飲むのをやめましょう。
こと typically deals with more abstract, distant concepts. Cases when only こと is allowed:
1) When the following clause deals with internal thought or communication: 明日の授業に出られないことを先生に伝えてください。
2) When you are nominalizing a single sentence (=the following clause is です/だ/である) - a.k.a. "N1は/が N2だ" pattern: 私の趣味は走ることです。
3) Set phrases and grammatical constructions such as ～ことができる, ～ことにする, etc., always take こと.
All other cases, including 好き / きらい, can have either.