I don't practice any Indian martial arts, but fighting is fighting...
One can use footwork, spacing, and timing to avoid being struck - and deflections/blocks with the blade if necessary. When at a diagonal to the enemy, you aren't in their optimum striking area and they must adjust to both attack and defend most effectively - there they are vulnerable. One can use spacing by being just within range of the enemy, then leaning back (like a pendulum affect) to avoid being struck and then leaning back in to destroy the enemy. And timing... angling away while striking at the enemy arm, wrist, hand, knee, etc. while their strike is coming is a good "buzz kill" for your opponent. Of course blocking and deflecting with blades isn't ideal but there's different techniques for that as well. And of course, do not forget kicks to the groin, knees, and shins when close. If you have a superior angle, timing, and cripple the enemy's rooting - it's hard for them to effectively attack you. Also, anyone mid-movement or in transition is vulnerable to an attack - thus if your timing is on point, you can catch them at the moment they are least prepared to defend. Fakes and feints are also useful. THere's a whole arsenal of tactics and principles - obviously however, a shield would help a lot, though it makes it harder to grab.
In Chinese martial arts, when concerning the dao/saber, they say when dan dao (single) watch out for the free hand ('cause of grabbing), and when shuang dao (double sabers) watch the feet...
But then again, in military settings Chinese have often used shields - it's usually in civilian settings and late-Qing/early Republican that swords were used without shields
How do you think the katar-tulwar warriors do it? Katars aren't the ideal blocking tool either...