build a 125 khz oscillator
Ok,
This is clear.
You could do this thing using read only tags (EM4100) or read/write tags (AT5567). In order to comunicate with the tags you could use an ic like
EM4095, 4,2 - 5,5V.
or HTRC110 (SPI controlled), 4,5 - 5,5V.
First of all you have to decide of what type of tags are you going to use. You could do this job with both read only or read/write tags.
Using read only tags you have to learn the cards 64bit id to the door lock using let's say a button. Then whenever the door lock read this id, will open the door.
Using read write/cards you have to build a device for writing information inside the blocks, and also you have to address the door locks. So each door will have it's own address. Using the device that write cards you will write inside the blocks the address of the specific door. When a door reads a tag and the address is the same then the door will open.
I think that this was a very good help in order to begin with your research.