I checked around and I think there is a bug in the versions of the game where the three parts are spliced together in a single file (such as the Amiga one), revision 1.0.1. When you say to Emilia to take the oiler you get this:
> take oiler
- Nanna, can I please borrow you some tools?
- Yes, but do not leave them around after you finish.
You can't.
And the oiler is not in your inventory. However, if you continue, Emilia behaves like the oiler is with her! I did not notice this bug, as it appears only in the versions of the game where the three parts are spliced together. I always check that the game can be finished with a standard solution and it did. I haven't noticed the "You can't." message that here is indeed very confusing and incorrect.
I will correct it in the next week or so.
To continue playing, try with this sequence from start of part 2, it should work:
n
n
w
talk to father
read letter
read message
e
s
e
talk to voicepipe
push button
w
n
talk to nanna
s
s
open the door
e
activate compressor
x compressor
open valve
w
n
n
x bench
take oiler
s
s
e
put oil on the valve
open valve
activate compressor
Let me know if this lets you continue playing.