...[one time I dodged a guy]...(snipped)
(I usually don't attempt to reverse engineer what happened in a fight to translate it into mechanics, but sometimes I do -
Can your game of choice tell this story?)
As I have said quite a few times now 
it's not impossible to dodge, it's just much harder than parrying. If you want a viable dodger, there are ways to do it, either through the "Daredevil" combat trait which allows the practitioner to stay or land on their feet while evading, or by substituting the professional Acrobatics skill, which you can use instead of Evade and keep on your feet. An evade in this manner is still harder to pull off because as a defence the defender has to beat the attack in an opposed roll instead of a "straight" successful roll. To succeed when facing an opposed test is to roll higher than your opponent rolls their attack, but still succeed yourself. In contrast a parry just needs to succeed, even if the attacker also succeeds, the parry will block the blow as long as the weapon is large enough.
If the GM or players absolutely can not stand dodge to be inferior to parry they could remove the requirement for the dodge to succeed as an opposed roll, but this then makes dodging superior since it's not affected by weapon size, and as a consequence removing one of the nuances between dodging and parrying - dodging is harder, makes most people prone, but will protect completely against any size of attack, a parry or passive block is easier but is limited by whether the defending weapon is of an adequate size.
Secondary thought: It's not so much about being "unarmed" as the fact that there is a lot of nuance to range when you engage in hand-to-hand combat. Assuming they're unarmored, a dagger fighter is pretty thoroughly screwed against a swordsman, almost as much someone who's unarmed. Same holds true for the guy with a one-handed sword going up against a two handed one, or a two-handed sword vs. someone with a staff/spear/polearm.
True but you are mixing here dodging with parrying, weapon reach and size, all important but different than the issue of dodging. An unarmed fighter can parry with their limbs, which are classed as small weapons as far as size goes.
But trying to "accurately" model that stuff is a really tricky thing to account for, and people in fantasy tend to like dagger fighters. So most games gloss over it. IIRC, from what I read of the rules, Mythras does actually separate out combat range into "close," "melee," "reach," and "ranged," which is definitely much more thorough than most.
Yes and no with that. Mythras does model weapon Reach and weapon Size, with different weapons having different sizes and reaches, but it does not represent different ranges as such. In terms of melee you are either engaged or unengaged, this does have consequences, largely whether you can move freely or not. Ranged weapons can be used at any range at any target but there may be penalties depending on circumstances. The important question as far as weapon reach is concerned is - "at what weapon reach are you engaged at?"
If you are engaged in melee, then weapon Reach comes into play. If the difference between the weapons is
two steps of reach different. For example, a dagger (short) Vs a longsword (long) is two steps, which means the dagger fighter is held at long reach and may only attack the weapon itself, not the longsword fighter. The longsword fighter may attack the dagger fighter directly. The dagger fighter may defend themselves by parrying but, and here is where weapon size comes in, if your parrying weapon is one size smaller then you will only block half the damage done, and the dagger is one size smaller (small dagger compared to medium longsword).
The situation is not hopeless for the dagger fighter, because if they win a special effect, they may Close Range to wherever they like, and if they want to strike that will be Short range. In this circumstance the longsword fighter is at an immediate disadvantage, they can not parry with the longsword at all, their effective weapon size is reduced, and their damage is reduced to represent the pommel or haft of the weapon (1d3+1). The longsword fighter may of course drop their weapon to draw another more suitable, or try to re-establish their range by winning a special effect themselves and getting the engagment back to their preferred Reach.
This is another advantage of a weapon and shield combination especially something like a spear + shield, the spear has a Long reach, which will keep Short reach weapons away (daggers, clubs, maces etc) and the shield will still work fine as a parrying weapon even if an opponent gets to Short range, because all shields have a Short reach.
When I've run games online I have rarely used the Reach rules for a couple of reasons - generally, combats don't have weapon differences of two steps of reach or greater, so it tends be rare, I also find it a bit too much to track. I'm in the minority since other GMs I've heard from do use it and don't have a problem tracking it. Weapon size on the other hand is not tricky to track and it comes into play all the time. Not using reach does reduce tactical subtlety, dagger fighters, for example,
can be effective, if they can get within their preferred reach, the same with grapplers and unarmed fighters generally.
Weapon size only needs a difference of one size to make a difference. A weapon one size bigger than the parrying weapon will still do 50% of their damage to a target, two sizes bigger will get through the parry to do 100% weapon damage. Many two handed weapons are lethal against almost any one handed weapon because they have a size of H (Huge), almost all 1h weapons are size M (Medium) at most, except for shields, which are mostly either H (Huge) themselves, or L (Large), with only the buckler having a size of M (Medium).
Just a parenthetical note on gladiators - there is a Fenix magazine Mythras article on suitable combat styles, with appropriate armour and combat style traits for a range of gladiator types
http://thedesignmechanism.com/resources/Fenix 1402 RuneQuest.pdf
