Are the tongues necessary? Can I just take my circular saw right
between the boards, cut them way, and then screw them back down
afterward?
You've been misinformed. The point of tongue-in-groove planking is to keep the floor boards from twisting, slipping and sliding against each other and squeaking (or squeaking more in your case). You still need to secure a tongue-in-groove floor to the subfloor or joists.
Joists almost never squeak on their own. Squeaking comes from two pieces of wood rubbing against each other - usually because a floor hasn't been adequately secured.
Now if you DO need to cut away the flooring, then you should cut along the seams, and then buy Hardwood Floor Spline and rout out the old tongue so you end up with two grooves facing each other, and use the spline to rejoin the flooring when you reattach it.
But BEFORE you do that, I'd get a bunch of 2" coated screws and drop them through the subfloor into the joists below and see if that fixes the squeak. It's subfloor so you don't care about the face, and if it doesn't work, they're easily removed.
*Tip - use a hammerdrill when putting in the screws
The plywood goes down so the groove is away from the wall, that way, after the row is finished, or at least when you decide to start the next row, a 2X4 can be placed across the joists at the edge of the next row and drive, with a sledgehammer, the second run into the first. The gap should be 1/8" between ends. The tongue and groove (T&G) of the sheets should be driven snug. Do not try to drive them tight, although in some cases it might be needed in order to keep a straight run. The first run is set to a chalk line, but the rows after that can start to meander after a few runs are down, and to correct it with a tighter fit or if need be, a loose fit to correct the run so it remains true
The subfloor adhesive I choose to use is polyurethane based adhesive. It has a long open time, Meaning you don't have to rush to get it covered before the glue "skins" over, thus minimizing the bond. Also, it is twice the cost of regular subfloor adhesive, but you can actually use less. Since there is no "skin" that will form that will need to be broke again by the laying of the plywood over it, to squeeze the glue again out of the skin that was formed by it sitting open before the plywood goes down. Do not drop the plywood on the glue or set the plywood off the final placement too far or firstly the glue will splatter all out off of the joist, or slide or scrape the glue off the joists. I seen both of these things happen in my years of construction. Needless to say the bond will not be worthy. The tongue or the groove does not need to be glued, although there is no reason not to. Some engineers require it in certain applications, but for standard subfloor applications none will be needed. Again it is to your discretion also. If you choose to place the glue at the groove, so the tongue drives it into the groove.
Screws are the best to secure the plywood with, and since a premium glue is used, there only needs to be enough set to draw the plywood to the joists. You can still place them as it has been done before the days of glue which is 6" on the edges and 8" in the field.
With glue you really can spread them out farther, 5 screws used on the ends if you choose, and 4 across the field. There are drills that are sold that use screws that have the screws collated in coils or strips. Makes this go much faster. Rental is an idea here.
Again with the glue, nails can be used too, since the glue will do all of the holding after it has set. Air powered nailers are available for this and will be faster than screws, but the nail gun in some cases does not draw the wood together like screws.
Best Answer
Wood moves over time, no real way around that. The board could have been fitted so tightly originally, that over time it expanded just enough to force it up.
As already suggested, you could trying smacking it down with a piece of scrap wood and hammer. If that works, there are special screws you can use to screw the board down more permanently. The screw head is designed to break off to make as little of an appearance in the board as possible.