I am still in the beginning stages of learning japanese grammar and while I understand the meaning of the kanji I don't understand what のも means in the context of this sentence. 自分で言うのも なんだ けど
- This の is a nominalizer. 自分で言うの = "saying it myself"
- Here も is used in place of the topic marker は. Doing so makes a sentence a little reserved or mild, similarly to English "well", "kinda", "a bit", "(not) quite", etc.
- なん here basically means "weird". More generally, 何【なん】 can be used to avoid saying negative words directly in conversations.
See Schokolade's links for more information. Put together, 自分で言うのもなんだけど literally means "Saying it myself is a bit weird, but ...". It's a set phrase used before you want to say something you should not say. "I may not be the right person to say this, but ..." or "Though I say it myself, ...".
The 「の」is a foraml substantive in the sentence.
It mean 「のこと」、「のもの」、「のほう」, etc., making the attributive form have the same qualification as a substantive, but we generally don't say it completely for convenience.
Here 「も」is used to avoid expressing one's opinion directly, making a sentence mild.
The whole sentence means "I shouldn't / don't want to say this, but...".