Can indoor cable be used under a patio roof?
Code considers areas normally dry to be ok for nm cable 334.10.A
under your roof is one of those locations that Is not subject to dampness or wetness some jurisdictions consider a porch a damp location it usually depends on the roof type for example a normal 3 tab roof with tarpaper is considered a dry location, but a roof with corrugated plastic and even metal if not insulated is a damp location. If you use a GFCI in this location it needs to be WR weather rated the electronics are coated to protect them from moisture and they can not be located above 5’7” but they can be used to protect the load side.
I would think as long as above 8’ exposed romex or NM cable would be allowed by your description soffits &amp; normal roofing.
Updating because of change to thhn;
Where damp or wet THHN /THWN cable (almost all thhn is dual rated but thwn is the wet rating) needs to be used. Your circuit will need to be in conduit box to box 1/2” will be fine for your setup.
All wiring methods below 8’ require protection but THHN requires conduit from start to finish.
The reason most home owners use UF and NM wiring methods is because 12&amp;14 gauge circuits with thhn requires 3 different colors hot usually black, neutral usually white, and ground usually green.  (Hot can be any color other than gray, white, green. Neutral can be white or gray , ground can be green or bare).
Home owners usually use pvc conduit as it is easy to cut and glue. From your box there can not be more than 360 degrees in bends or 4 90’s wire pulls get tough after 3. If you need more than 360 a conduit body is Normally installed I use a conduit body at a 90 in many cases called an LB, LR or LL  the hole being back , right or left. There are also form C body’s that are inline , a box can also be used.
The one thing I see home owners do wrong in most cases is the wrong kind of box. Outside a bell box or weatherproof box is required unless recessed in the building structure.
The pvc conduit needs a strap within 3’ from the box and supports per table 352.30 1/2”-1” max space 3’
These are the additional things to think about but should get you on your way to a safe instal of your lights and receptacles.