Make and model of the DMM?
Whenever you run into these crazy conflicts, you have to stop and reexamine everything, including your own assumptions. It seems that you are testing everything correctly, but check these:
1. DMM polarity. Some DMMs have reverse polarity for resistance, but I've not heard of one that is reversed for diode checks--but tell us what you have. And in case gremlins have rewired it, do you have another DMM that you can use to absolutely verify that the diode check polarity is correct?
2. Another component. Do you have any other semiconductors you can quickly check to verify that your measuring system performs as expected?
3. The datasheet. Make sure you have the correct pinout. The base is the center terminal from what I can see, so this is probably a non-issue.
I have one of those cheap-o multi-component testers that I often use just for a final check before I install parts in repair projects, just to avoid silly problems like you are having. Absent some pretty unlikely scenarios like the ones I just listed, it looks like your transistors are mismarked. Or, they might not be BJT transistors at all.
https://www.ebay.com/itm/Green-12864-Mega328-ESR-Transistor-Resistor-Diode-Capacitor-Mosfet-Tester-w-hook/322498217999?hash=item4b1664480f:g:c8EAAOSwCQZZA8gO