First we need to determine the Grease spells area:
Slick grease covers the ground in a 10-foot square centered on a point within range
Then we need to determine what "enters spell area" means. I did not find clear definition, but if you fly over the area of Grease spell, it'd take a special kind of DM to consider that "entering".
Looking at other spells, Thunderwave clearly specifies an area that is a cube. So I think the normal English meaning of Grease spell's area is quite clear: there is a thin, almost 2-dimensional square layer of slipperiness covering the ground, and to enter it you have to basically touch the ground. If the area of effect had a volume/height, the spell would say so, talking about cube or cylinder.
So, if your feet do not even touch the ground covered by the Grease spell effect, you are not entering it. If you jump completely over it, you won't touch it. So jumping far enough avoids the spell.
Then about STR 10: Strict RAW, with STR 10, you cover only 10', not 10' + one step. If you keep just jumping, you advance 10' per jump, which includes the space taken by your feet. If you kept jumping, you would move forward in 10' increments (well, less for standing jump, but the same principle applies).
When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump.
So you'd have to either jump from or land at the greasy area, and while you might avoid the difficult terrain (because you don't actually spend movement walking in the grease), you'd at least need to make a DEX saving throw. With this reading, you'd need 1 (or even 2, one at both sides) extra foot, in other words STR 11 (or 12), to avoid the grease completely by jumping.
RAI, hard to say. The rule could be interpreted meaning, you can jump past an obstacle of that many feet, and a DM could reasonably rule it that way. The argument for this interpretation is, that the rules don't say how many extra feet of jump distance you need to get over an obstacle like this, so the reasonable ruling is, that no extra feet are needed.