More information is required.
First, yes, absolutely, thermostats get stuck open or closed. The description from @jseyfert3
above is pretty good, except there needs to be some more emphasis. If it's stuck closed, you WILL overheat your engine, WILL warp the head and WILL blow a head gasket, totaling your Sienna. Maybe that will make the "where to put money" question much easier, because it will be put into a new car payment.
Second, I'm not entirely clear... "Went and bought thermostat then in went off." sounds like the light went off WITHOUT you actually replacing the thermostat. If so, we can start at the beginning, which is actually a MUCH better place to start to look for advice on cars.
So, we start with, what code(s) do you actually have? What were the symptoms? What made you decide you need a new thermostat as the best, first solution? Have you checked your coolant level? What's the deal with the oil leak? Is the money issue that there other car issues which cost money or is it other money issues limiting your car expenditures? If it's other car issues, what are they?
Honestly, I didn't even know there was a code for the thermostat. It has no wires, so I'm not sure how it determines it, unless it's by pressure/temperature. Typically stuck open never warms up and stuck closed never cools down (overheats). There's a third option where the temp is off and it will open too soon or too late but not enough to actually make it super obvious unless you have a live temp readout from a scan tool. All that said, the most important, critical first task to ANY coolant issues is to check the coolant level and inspect for visible leaks. The level check needs to be done carefully, as, you can't check the actual radiator level and the overflow tank often get stained with coolant, so you can't necessarily tell. I find it best to bounce the van so I can see the fluid level moving in there. Now, the way the van pulls coolant from the overflow is that you bring the van to operating temp, then let it cool, which creates a vacuum, pulling in excess coolant from the overflow. If you have a leak, it can pull in air instead of coolant, which is where leak detection comes in. You want to look carefully on all sides of everything with bright lights for the telltale pink crust or evidence of wetness.
Assuming you have a full coolant symptom, it's time for a test drive. Put front and rear heat on full hot, high blower and take the van for a drive. You want to get it up to operating temp. If you have a scan tool that gives you live data, you want to track/monitor the engine temps. Typically, what you expect to see is that it will start at ambient temp, climb to a temp (80-84°C/176-183°F), then drop maybe 30 degrees, then climb, then drop less, and so on and so forth, until, eventually, it reaches an equilibrium state somewhere around 20 minutes (less, if it's highway speeds) of driving time. If the temp never gets to the "normal" range, or it climbs far, far past the normal range, you have a thermostat issue. You will want to change it out ASAP. Best case scenario is that it's stuck open and you will find your gas mileage is down in the 10 mpg, which effectively doubles your cost of gas. At $3/gallon, it won't take many miles before you pay for the cost of the labor on replacement. Worst case, it's stuck closed and your playing a game of "how far can I push it?" before you overheat and destroy your engine. Side note, you can often "fix" (very short term, in an emergency) the overheating from a bad thermostat by turning the heat on full blast to add additional cooling to the system which can draw some heat out of the coolant.
As for an oil leak, I would entirely ignore it for now. If the van is dripping on your driveway, throw down some kitty litter or put a piece of cardboard down every time you park. Carry a jug of 5W30 in your van at all times and check the level once per week and top off as needed. You can drive essentially indefinitely like this without causing damage. When you're ready to do a valve cover gasket (assuming that's what you meant by "vent cover gasket") job, there's a bunch of other work to do at the same time, so it's best to give yourself plenty of time/money to do the whole job, rather than trying to just do part of it. Of course, depending on other issues/factors with your van, my position on this may change.