Water coming in through the walls of an old concrete garage
It sounds like your garage is the low spot in the landscape and making a drain system difficult or impossible.  If you are sure that drains aren't possible, the only other possible solution may be treating the interior wall surfaces with an epoxy wall treatment like "Dry Loc".  Dry Loc will withstand hydrolic pressure of about 3psi, which is usually enough for walls and floors effected only during times of heavy rain etc.  The trick of making this stuff work well is to be sure the concrete is dry and any loose, flaking or effluence is removed. Obvious cracks and foundation form pins must be "keyed" and filled with hydrolic cement such as "rocktite" before painting the Dry Loc on.  The Oil based Dry loc is much easier to use than the latex based version, but lots of ventilation is needed, which should not be a problem with a garage. you will probably need two coats and be sure to work it into all the tiny holes etc, 100% coverage is important.   Good Luck.