If I don't have Entrenchment or Diplomacy, can I play online against other people with Entrenchment or Diplomacy???
No. Do note that you need to buy Entrenchment first before purchasing Diplomacy since Diplomacy uses all of the Entrenchment content. (In contrast, the upcoming Sins Rebellion expansion will be stand-alone and will include all of the content of the previous games.)
Does anyone else just have the original Sins w/o these mods?
The player counts on the Vanilla/Entrenchment server are lower than on the Diplomacy server and almost all of the people on the Vanilla/Entrenchment server are just playing comp stomps with their friends. The real action is on the Diplomacy expansion.
Do these mods completly change the way the game is played and would I have to devise completely new stratagies?
you would have to learn about starbases, how and when to use them and how to deal with opponents' starbases. Whether or not a starbase(s) will come into play depends on your opponent(s), his race, his strategy, the map, and what's going on in the game. The Diplomacy expansion didn't add all that much to the online multiplayer PvP game but in some games the Diplomacy additions come into play. (The Diplomacy expansion was aimed primarily at people playing AI.) One big difference is that you need to conduct research before you can feed credits and resources to allies.
And lastley, is the game considered more difficult to win with these mods, or is it easer, or would it be about the same as just the original Sins w/o mods?
If you're playing against human players in online multiplayer I don't see what difference it really makes. It's just as easy or difficult now as it was before. The pro players are still pros, etc. If you're only playing against AI, the Entrenchment expansion makes it easier because the AI is a foolish opponent and it has no idea how to properly use or deal with starbases. So in many cases you can simply allow the AI to suicide itself on your starbases. The Diplomacy expansion adds two new AI cheat levels, Cruel (4x economy buff) and Vicious (6x eco buff). They're pretty challenging and you'll have to rely on having the AI suicide itself on your starbases.