Those の are nominalizer, which makes a sentence into a noun equivalent. のは＝の＋は <日本語> は　むずかしいです。　Japanese is difficult. <日本語を話すの>は　むずかしいです。To speak Japanese is difficult. のが＝の＋が <勉強>が好きです。 I like studying. <日本語を勉強するの> が好きです。 I like to study Japanese. のを＝の+を <たばこ>を　やめます。 I quit smoking. <会社でたばこをすうの>を やめます。 I quit smoking in the office.

１．わたしはあるくのはいやです　I hate to walk. - might prefer take a bus, taxi, or something. ２．わたしはあるくのがいやです I hate to walk. - just don't want to 'walk’ In this case, 「～は」implies there are some options, 「～が」emphasizes　’～’. ３．わたしはあるくのをえんりょします　I would rather not walk. ( えんりょする　is a polite way to refuse) 「を」is objective use. Usually,「です」comes after nouns, pronouns, adjectives. 「ます」comes after verbs.

Thank you so much for posing this question because for a long time this has really confused me. It was absolutely terrifying searching through countless books just too find the correct answer to all of these variants. It's still quite confusing to understand going by the different answers here in the chat. 😅

See "The 「の」 particle as explanation" in http://www.guidetojapanese.org/learn/grammar/nounparticles

たとえば 1.わたしのはこれです(わたしのものはこれです) 2.あなたのがこれです(あなたのものがこれです) 3.寒いのを　がまんします(さむいことをがまんします) Good luck :)