Negative Volitional?

I know the volitional form is like saying "let's ~". Is there a way to make a negative volitional, "let's not ~", or would this simply be done with negative froms ~masen and ~nai, and context decides that it means "let's not ~"? Yoroshiku onegaishimasu.

There are actually a couple.

1) ～しないでおこう - shinaide okou (okimashou)
EX:戦争しないでおこう - sensou shinaide okou (lets not go to war)

2) ～ないようにしよう - nai you ni shiyou (shimashou)
EX:怒らないようにしよう - okoranaiyou ni shiyou (let's not get mad)

3) ～のはやめよう - no wa yameyou (yamemashou)
EX:公園へ行くのはやめよう - kouen e iku no wa yameyou (let's not go to the park)

another one

～の（は/を）よそう

ありがとう！
Are there any nuance-charged differences between using these and when it's appropriate to use them?

Explanations

I was going to elaborate on it in my first post but I am not 100% sure, so take this with a grain of salt. Also, remember that the volitional form can be used for "let's" but also for "you/I should". Like "doa wo akemashou ka?" does not mean "should we open the door".

1) ～しないでおこう - shinaide okou (okimashou)
Literally: "let's leave that undone" If you know the base form, [shinaide oku] this is a little bit easier to understand. For example "shigoto wo shinaide oku" meaning "to leave one's work unfinished". So this one is something more like "let's move on without doing that"

2) ～ないようにしよう - nai you ni shiyou (shimashou)
literally: "Let's/you should make it so that we/you don't X" This one kind of has a "let's avoid doing x" connotation

3) ～のはやめよう - no wa yameyou (yamemashou)
literally: "Let's/you should stop doing X" This one is often used when changing a plan like "Let's give up on going to the party (cause the traffic is awful, or whatever)" or with suggesting someone should stop doing an action "Why don't you stop smoking."

4) ～のはよそう - no wa yoso (yoshimashou)
litterally: "let's/you should quit/restrain yourself from doing X" This one is used more for resisting or avoiding a certain course of action.

There, clear as mud, right?

Thank you very much! I'll be writing these down as well as their connotations! Just one thing related to #1...

~shinaide okou.
Just the way you made it sound, it sounds as if it's only applicable to suru verbs.
勉強をしないでおこう ー 正答
食べないでおこう ー 不正解？
This probably isn't the case, but I must check.

No, I just chose to use a suru verb as an example. It is fine with both.

Also, sorry for writing so much in Romaji. I wasn't entirely sure of your level because you didn't use any kana in your original post.

自分の例文はどうですか？ how are my example sentences?

1. 宿題を全部終わらないでおこうよ。Let's not finish all the homework (and move on to something else).

2. 学校へ行くと校長に突き当たらないようにしよう。When we go to school let's avoid running into the principal.

3. 複雑すぎるだから、中国語を習うのはやめよう。We should quit Chinese because it's too complicated. (do I require a の after すぎる?)

4. 彼がそれをしなかったで、怒るのはよそう！ He didn't do that, so don't get mad!

1)
宿題を全部終わらせないでおこうよ/終えないでおこうよ。

終わる is an intransitive verb (although 終わる can be used as the transitive in some cases). You need to use the causative form 終わらせる or the transitive verb 終える.

2)
学校に行くとき、校長先生にぶつからないようにしよう。

3)
中国語は複雑すぎるから、習うのはやめよう。

4)
彼はそうしなかったんだから、怒るのはよそう。

やめよう and よそう are interchangeable in most cases. やめよう sounds more colloquial.

Thank you for helping me to sound more natural!