Sorry for the delay, I don't work at the weekend.
If you create post types for Songs, Lyricist, Singer, Music Director, Video Director then you can create many-to-many relationships that all connect to Songs as the anchor, e.g.
Songs <<>> Lyricist
Songs <<>> Singer
Songs <<>> Music Director
Songs <<>> Video Director
Let's take the example of the Lyricist, and you can replicate the same steps for the other relationships.
To recap, when you view a single Song post you will want to display the name of the Lyricist with a link to the Lyricist post.
When clicking that link and going to the Lyricist post you will then see a list of all the songs written by that Lyricist.
So you will need to create a template for Song posts, and a template for Lyricist posts.
To display a link from the Song post to the Lyricist post you will need to create a View (because this is a many-to-many relationships and there could be more than one Lyricist).
So create a View where the content is Lyricist posts, and which includes a relationship Query Filter to select Lyrics posts from the Songs-Lyricists relationship that are related to the post where this View is shown.
In the output section you will output the post title as a link (using the wpv-post-link shortcode). You might want to use the Loop Wizard to output this as a comma-separated list, for example.
Insert that View into your template for Songs.
Now create another View to display all of the Songs written by the Lyricist we are viewing.
So the content selection will be Songs, and you will again need a relationship Query Filter, again showing posts from the Songs-Lyricists relationship related to the post where this View is shown (i.e. Songs related to the current Lyricist).
You can then output whatever fields you require from the Songs, e.g. the titles as links.
That's the basics of being able to go back and forth from Songs to the Lyricists then back to the songs written by that lyricist etc., and you'll need to set up something similar for each relationship.
For background, here's the documentation about Post Relationships within Toolset: https://toolset.com/documentation/post-relationships/
If you get stuck on something specific, please let me know and I'll be happy to help.