Will gtx 745 work with my 240w psu?

It will likely work,

I CANNOT say for certain without the full specs of your PC (CPU, motherboard, hard drives, exact PSU model, etc), but:

The GTX730 is rated for 50 watts of power consumption delivered over PCI-e, while the GTX745 is rated for 55 watts over PCI-e. 5 watts isn't a lot (a standard USB 3.0 port delivers around 4.5 watts for reference)

I highly doubt any manufacturer would use a PSU with less than 5 spare watts for the system.

You're not going to have much of a performance increase from upgrading from a 730 to a 745, I would consider switching to a higher end GPU and PSU.

1. you can ALWAYS replace the PSU

2. the gtx 745 needs a MINIMUM of 300 watts

3. CHEAP psus (which ALWAYS have less than 500watts) are VERY bad, they can fail destroying your computer

4. get a GOOD psu (a 80+ silver or gold) and it will last for years

That power supply isn't meant to run a graphics card.

Nope, you will overload the PSU, if it even powers up...

you would want at least a 450 W supply.

Get at least a 500w.

No. 300w minimum.