LGA 1366 is an old socket, why not go with the latest 1150? Finding an i7 for less than $100 USD will also be hard to come by. So you're willing to spend $150 for the motherboard and $100 for the processor? So in total you're willing to spend $250? If so, I'm going to allocate the funds a little differently.
Will you have a dedicated/discrete graphics card? You will need one for the Xeon, which provides similar performance to the i7-4770; however you'll need to stretch your $250 budget by $47 unfortunately:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Xeon E3-1231 V3 3.4GHz Quad-Core Processor ($247.98 @ SuperBiiz)
Motherboard: Gigabyte GA-H81M-H Micro ATX LGA1150 Motherboard ($48.99 @ Amazon)
Total: $296.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-29 20:59 EDT-0400
As mentioned you'll need a dedicated/discrete GPU, or there will be no signal on your monitor; this is true as the Xeon processor does not have integrated graphics, however as mentioned, it provides similar performance to the i7-4770.
Otherwise if you're not planning to have a dedicated/discrete graphics card, then purchase an i7 which has integrated graphics. However purchasing an i7 will go out your budget of $250; if you're willing to spend $270 ($20 more than your budget), go with the following:
Intel Core i7-2600K for $230 from eBay and purchase a cheap motherboard, such as:
Motherboard: Gigabyte GA-H61M-HD2 Micro ATX LGA1155 Motherboard ($39.99 @ TigerDirect)
Total: $39.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-29 21:05 EDT-0400
The i7-2600 is a second generation i7 and is more modern than the i7-920 you desire, with that said, second generation had a major performance boost over the initial first generation. I'd spend $20 more with the i7-2600 I suggested.
All the best.