There are a lot of factors that go into how long it takes to get to 99 str. I can't tell you exactly how long it took me, but it was a long time. Of course you will need to have a high atk level as well if you want to level your str quickly, and a decent defence so you can make longer trips. Because of these factors it is almost impossible to give an exact time to get to 99 str.
My favorite method is to fight armored zombies(lv.83). I wore a salve ammy(e)(+20% atk and str against undead), a saradomin sword(best str trainer), and the highest str increasing equipment available(void robes with the melee helm, +15% atk and str, are the best if you have a good def level). This gets you the best str exp in the game(100k-250k/hour depending on your level), but you don't get any slayer xp. The zombies are also near an altar so you can use your best prayers to train. You may use a whip and a dragon defender to get to 99 atk and def.
If you are going to use slayer to level up you will need to use the black mask(+15% atk and str when fighting current slayer monster). This method slows down your xp gain for str but like earlier stated you also get slayer xp. It is up to you.
Whatever method you choose make sure you drink atk and str potions. This will help a lot in the long run.