There is no specific strength limit (except the limit of the data type used to store the value, which is apparently an int and can therefore go up to 2,147,483,647).
There is, however, a finite number of units one of which is the strongest unit and a finite number of promotions which increase the strength. This leads to an effective maximum strength which may very well work out to be 70 when attacking in unmodded BtS. There are mods that add promotions which can allow the strength for a unit to go higher. There are mods that adjust the unit strengths. There are mods that add more powerful units like Next War, which comes with BtS and has the Assault Mech with a base strength of 60 and the Dreadnought which has a base strength of 70. And I can assure you that the promotions still apply the expected adjustments to a unit with a base strength of 70.
You should also note that when attacking only the Combat line of promotions actually increases your unit's strength. The other promotions' percent modifiers are applied as reductions to the target's strength (and/or reductions to its percent bonuses). In your screen shot the +75% from the six Combat promotions is applied to the unit's base strength of 40 for 1.75 * 40 = 70. The "+25% vs Melee Units" and the "+25% for hills (Unit Ability)" lines in the help actually apply to the target, which is why it is showing a strength that is not the unit's base strength of 6 since it gets +25% from being on a hill, that is then reduced -25% for being on a hill (due to the attacker's promotions) and then another -25% for being a melee unit giving it a net penalty of 25% which it applies as 6 / 1.25 = 4.8 since the base strength of a swordsman is 6. That is where the "70 vs. 4.8" line comes from.