Dhpub,
Just to make sure that you are having relationship:
1:N -> Project to Opportunity (mean lookup field in the Opportunity to Project)
1:N -> Project to Order
Assuming you already have this relationship, right?
Then from your Opportunity, you create Quote, after Quote Active, you won by creating the Order, once Order is created then Opportunity Closed?
In the Quote, do you also have Project?
Can I suggest you to create the relationship as well between Project and Quote.
Then if you are using CRM Sales process, no customization, please add mapping the mapping of the project id, between Opportunity to Quote and Quote to Order.
To add the mapping, go to Opportunity, find relationship 1:N, find Opportunity and Quote then add the Project lookup for mapping.
Do the same thing, now go to Quote, 1:N Quote to Order then also add the Project lookup for mapping.
So that Once the Opportunity then create Quote, the Project is also be mapped, then once create Quote then Won it, create Order, in the Order form also will inherit the same Project ID.
Hence, the result here, the Order and Project are connected, you can create subgrid between Project and Order and see your tied Order from this Project.
Anyway, assuming that your relationships between those 3 entities are same as I defined in the very first place only it will work.
Hope this helps.
Thank you.