There is nothing more fun than button mashing through the cutscenes and then blowing everything up without really knowing what you are doing! xD
But if you want to play them in English, exactly two games were translated and released in America. Both of them are on the Gameboy Advance, named "Super Robot Taisen: Original Generation" and "Super Robot Taisen: Original Generation 2". They might be at a GameStop somewhere, or on eBay. Emulators would be the best way to get those, if you aren't morally opposed to it or anything.
There are probably fan translations for other games on the internet, but you would need to have the proper emulator and ROM files for whichever game you would like to play specifically. A lot of them are on PS2, if your computer has the specs to run that, you might want to give those a shot and look for files for a translation. I'm fairly sure that I've seen internet communities around that translate games.
I own both OG1 and OG2, so I know those for a fact. The rest of this is kind of speculative. There are a whole lot of Japanese SRW games, so I'm not too clear. Good luck on finding what you want though.
Super Robot Wars was created in 1991.
Super Robot Spirits happened in 1998.
Super Robot Wars A happened in 2001.
Super Robot Wars Alpha happened in 2000.
Super Robot Wars NEO happened in 2009.
Super Robot Wars Destiny happened in 2003.
Super Robot Spirits was created on 1998-07-17.
Super Robot Wars A was created on 2001-09-21.
Super Robot Wars R happened in 2002.
Super Robot Wars W happened in 2007.
Super Robot Wars Judgement happened in 2005.
Super Robot Wars GC happened in 360.