I used to use ashless 2 stroke oil in my old TDI, which came from the time when the switch to ULSD was made in Europe and the high pressure fuel pumps had lubricity issues. While it did (apparently) lube the pump, I never had any other benefits.
Smoother running engine? The V6 TDI from Audi with the well built and shielded interior was as smooth as a V6 gas engine, inside the car you never ever had the impression at any time that it was a Diesel.
Did it help against the injector issues that engine from 2005 was known for? No, not at all. I had to replace the injectors (all 6 of them) because of worn needle seats at the same mileage as others that never used 2stroke oil in the Diesel. The difference between my injectors and from others V6 TDI's which haven't used 2 stroke oil in the Diesel was there, but miniscule.
Did I gain or loose mileage? No, not at all. Not better, not worse.
Differences at the Diesel filter that may lead to conclusions of cleaning the fuel system? None.
Camera images through the injector holes - I expected a perfectly clean piston. No, didn't happen. Diesel Engines are dirty at the end of the day.
Furthermore you could - albeit slightly with the V6 TDI - feel that if you dosed over a certain amount you lost some power. Apparently 2stroke oil in the diesel alters the timing of compression ignition.
Cleaner EGR: In theory the EGR system should be cleaner because of the supposedly cleaner burn. No, didn't happen. My EGR was a complete mess, so was my intake system. After 100.000 miles with 2 stroke and cleaning additives in the tank: A gooey, sticky, sooty mess. What does help here tough is regular disassembly and manual cleaning with EGR cleaners.
With the new Euro6 with SCR catalyst Diesel I'm currently not using any 2stroke oil in the diesel. First, by now pump manufacturers should have learnt to deal with ULSD and then I haven't done enough research wether the Euro6 compliant DPF with SCR and Adblue (=DEF) is "unfragile" enough to deal with the extra 2stroke oil. Even tough most 2stroke diesel users claim that 2stroke combusts more complete and cleaner than diesel itself.
I did use it at 640:1 in my motorcycle as well, (Suzuki Boulevard C50, Piaggio 125cc scooter). The piaggio left a 2stroke smell and slightly blue faint out of the exhaust when left to sit for longer periods (more than a week), the Suzuki didn't. But both of them had a visible black soot layer in the end of the tailpipe. When ran with pure premium gas they didn't have that much soot in the end of the exhaust, only slightly and lighter in color.
Tried it in my sisters 125cc scooter, aircooled 4 stroke, around 500:1, after a few hundred miles it left residue in the exhaust that smoked after being shut off. I manually cleaned the exhaust and left the 2 stroke oil out. Clean exhaust ever since. Residue was minimal, but still there - which means it covered the catalytic converter. Nowhere near as bad as a real 2 stroke exhaust, really minimal only compared to a real 2 stroke, but it was there.
Tried it in my fathers car, 2.4 JTD with no DPF. At the yearly emissions check, I should in theory have seen a better result. But I didn't. The results were not worse, but not better. The ppm of soot out of the exhaust get measured via a sond in the exhaust, max acceleration from idle to rev limiter.
Honda GCVx lawn mower: 2stroke oil added 640:1 compared to Shell V-Power gas alone: With 2 stroke I can see blacker soot around the exhaust holes than if I run Shell V-Power gas by itself (less and lighter in color soot at the exhaust holes). The lawn mower when cold started always gives a nice small blue 2stroke smell small cloud at startup that disappears immediately. But it is there, even at 640:1.
From 2012 on I used to believe that a little 2 stroke in the diesel as well as gas, for gas there's a long, long thread at ls1tech.com. Nowadays, after all my observation started with my TDI over my motorcycles as well as lawn mower I'm more sceptical than convinced. I never saw the improvements I should have seen according to 2stroke oil in 4 stroke engine users, but I saw more negatives that I wasn't supposed to see.
So nowadays I run premium gas/diesel and at every yearly service I add a can of fuel cleaner treatment.