Since you have done math previously, the best way to ramp up rapidly is not through fluff material geared towards beginners and to focus on stuff that will actually force you to learn. You might have noticed that the only way to acquire mathematical intuition is to solve lots and lots of problems.
One possible path to follow:
1. Start off with Sheldon Axler's Linear Algebra done right. This is a more theoretical book (than Strang) but should help keep you challenged and motivated. Work through most of the problems. The best way to attack the proofs is to do them yourself.
2. Feller is the best probability book barring none. This is the kind of stuff that Persi Diaconis went through. Solve as many problems as possible but remember that trying to finish it all will take you years.
3. An excellent introductory stats book that doesn't assume you are an immature child is Freedman's book on statistics. This focuses less on the math and more on what statistics really means. Techniques in stats are fairly trivial but using them right is hard.
4. Calculus is useful stuff. As you go through your probability education, you will eventually hit the world of continuous probability which requires a good amount of calculus to go through. Spivak is an awesome book which should prepare you for that.
5. Learn some real analysis. Real analysis from the machine learning perspective is useful because a lot of measure theoretic arguments in research papers have underpinnings here.
