I don't think that strength is the overriding issue here. Yes you do need a certain amount of strength in your arms and fingers to play but there are many other issues with technique which are more likely to be giving you issues.
The best advice anyone here could give you would be to get a teacher, but I am guessing that there are reasons that you cannot do that. If you can do that then do so and get your advice from them.
Since I have no frame of reference for how competent you are currently I am going to assume that you can read music fairly well and that you have quite a lot of experience sitting at a piano and playing.
So there's the boring stuff: scales and arpeggios. Get a book - music schools (ABRSM, Trinity etc) all publish one so get one and start practising. If you are allocating 30 minutes a day to practise then do at least ten minutes to fifteen minutes of scales and arpeggios. Don't skimp: be critical of yourself and get them right. This is one of the fundamentals of your technique.
Pieces: Again the music schools can help here. All of them publish graded pieces for their exams so there is a source from which you can work out roughly where you are. Find the highest grade that you can play well (again, be honest!) and buy the books for the next grade. Work them up. Move on when you can really play them.
Studies: This is harder to judge. Many people swear by Hanon; personally I loathe them and feel that there are many better and more musical studies available. Czerny is popular and there are thousands of them, often classified by what they are trying to achieve. Also Cramer is very good and there are lots of others. But avoid the really big names, Liszt, Chopin, Scriabin etc. Their studies are mostly intended for showing off technique rather that acquiring it.
Hope that helps. Good luck.