Can I ignore resistor for IR LED?
Connecting two diodes in parallel:

No. Don't do this. The maximum voltage for the LEDs is 3V, and only for 100us pulses. 3.3V will more than likely ruin the diode, although it's unlikely that this will happen in practice. Putting only 3V across a single diode will draw 1A according to the data sheet. I cannot imagine the RaspberryPi will be very happy with this and will probably shut down or just brown out, reducing the 3.3V line down to something that doesn't break the diode, but also doesn't let you use the Pi properly.

Connecting two diodes in series:

This will probably be fine providing the diodes are not on constantly, and the on/off duty cycle and on-time limits given in the datasheet are observed. However, I don't recommend this. Two diodes in series will have 1.65V across them, putting the current consumption at ~300mA. If you add a normal diode in series you will drop the voltage across each diode to around 1.3, which puts the doide in the realms of 'normal operating conditions'. Asking if the resistor can be omitted suggests you have very few components at your disposal so I understand if you cannot do this, but you must understand the consequences of running components outside of their comfort zones.