I have a heavily token based deck. The tokens can usually become something between 5/5 and 15/15 in a few turns, but don't have trample. Is it possible for my opponent to be able to block all of my tokens attacking at the same time and they wouldn't take any damage? And no they don't have cards that specifically say that their creatures can assign additional blocking. I ask because if what I think is true, then if I have more tokens than they have creatures that can block, then I should be able to outswing them. Please I need clarification on this issue and any help would be extremely helpful.
Normally, each creature can block only one attacking creature. Some abilities can change this. For example, Brave the Sands has an ability that allows each of your creatures to block an additional creature, and Hundred-Handed One can block a hundred creatures when it is Monstrous.
Without any of those abilities, if you attack with more creatures than your opponent has, then if you attack with everything, some of your creatures will be unblocked and will deal damage to your opponent. For example, if your opponent has 5 untapped creatures and you attack with 7 creatures, they can block any 5 of your attacking creatures, and the other 2 will deal damage.
Tokens are not relevant here. When your opponent assigns blockers, he can choose to have each of his untapped creatures block one of your attacking creatures. So if you are attacking with more creatures than he has creatures available to block; he will not be able to block all of them, and the unblocked ones will deal their damage to him directly.
You should read through he basic rulebook; this is a fundamental part of how attacking and blocking work, so there's probably other important details you are missing: https://www.wizards.com/magic/rules/EN_MTGM11_Rulebook_LR_Web.pdf. From the section on Attacking and Blocking:
Each creature can block only one attacker, but multiple blockers can gang up on a single attacking creature.