There is the Sitecore Data Exchange Framework which allows you to import data from a source to a Sitecore Instance. Though, since you want to change the structure of the content tree where some items will be deleted and so on, I can see 3 options:
Implementation of a custom tool which takes as input the old Sitecore instance and create the new items in the new Sitecore Helix based instance.
You will create a mapper that will map the item from the old instance to the new one. Items that are not required are neglected.
By making use of SQL to directly creating / updating the items from the Sitecore databases. But this is very risky as you will need to first understand how the databases are structured and used.
Making use of Sitecore Packages. You can generate a Sitecore Package from the old instance, then modifies the project file and different paths found in the package. But this may be very difficult since the packages contains
Sitecore ID as path also
I will opt for option 1 because you will have more control on what you are doing. Also, it seems much easier to to implement the tool as you will already know which items are required and where you want it to be placed. Razl is not free and I am not sure whether it will help since it will allows you to compare databases but you will not be able to transfer an item to different location in the content tree.