To be clear: You cannot do this with the hardware you have on hand right now. It is not worth continuing with the Pi until you have additional hardware (or an alternate hardware solution entirely).
The Pi is capable of VLANs (wired only), but you need, at a minimum, a managed switch. Ideally you'd also have another ethernet port in the form of a usb-ethernet adapter.
The wifi on the Pi will not be sufficient for your needs if you expect to use these VLANs as additional SSIDs on wifi. Therefore, you may also need a wifi AP if wifi is indeed part of the equation.
As I stated earlier... the Pi is not a good choice for what you are trying to do...
(the implied thing here is that you find a device that is supported by OpenWrt -- this isn't hard to do, but you should do your research first).
VLANs are applied to Ethernet ports. For example on a regular switch, without VLANs configured, any devices connected will be able to talk to each other. When you do configure VLANs, only the Ethernet ports on the switch that have been assigned the same VLAN ID can talk to each other. That accomplishes network segmentation.
All that is to say, "VLAN" applies to switches or routers that has built-in switching capabilities. As I understand it, your project requires "network segmentation" between devices connected to your RPi AP. The simplest method of accomplishing that would be creating separate virtual bridges for each network segment, configure them appropriately bridge to upstream router, and have separate SSID for each virtual bridges. With that. device x connected to SSID p will only be able to talk to other devices connected to same SSID and access internet and be denied connection to devices on other SSIDs.
That is the general idea. It is your school project after all, so search around for documentation and learn how to implement them.