Its been said before, but you need to find a real 240V outlet, or have one installed. Most ranges (stoves) will utilize one. You could buy or make an extension to get to where you want. You could install another circuit providing a 240V outlet at the breaker panel, assuming there is room in the panel for another (double 240V) breaker.
Your welder also needs to be capable of running on 240v. Some can do both 120V (at reduced power) as well as 240V, but I think your Eastwood is 120V only. You typically have to pay a bit extra for the dual voltage option. You will probably need to upgrade here.
The other option would be to use a generator but that will set you back around $1500 for something with enough power. I have a Generac 8000 watt unit that is capable of running my 220A welder (on 240V), but it is loud and heavy, and ear protection is required. A (gasoline) generator typically needs regular maintenance, like switching out the gas each year, oil changes, test running, etc. Diesel is less maintenance but more costly and heavier. My generator is a backup for the house, which happens to also be capable of running the welder. I've only used it that way a couple of times.
Thanks for the rep
Even with that setup I don't think I have welded anything over 1/4 thick, although the welder is certainly capable of it. My welder is air cooled TIG, I would really need to step up to a water cooled torch to do anything heavier for any length of time. I suppose it could stick weld thicker stuff, but I generally like the TIG mode.