You can actually have all 17 types of Pokemon in just 1 party, with your starter and HM moves.

Here's some tips to create a team with 17 types:
* 2-typed Pokemon helps.
* Compatible to your "about to use TM" (if using some TM/HM).
* HM types also helps like Surf
* Considering all Pokemon has 4 moves to learn so 6X4=24,so all in all there are 24 moves with 17 types,you have 24-17=7 moves left or extras.
* This tip is optional, you can use status moves to catch Pokemon easier even in a high level like Thunder Wave,Sleep Powder, and False Swipe (False Swipe hurts the Pokemon but it never try to faint any Pokemon).Also you can try moves that is highly accurate like Swift or Shock Wave (any type would do) just in case you were use by Sand-Attack or the opponent use Minimize continously (the result is the foe is hit by ANY move until it's hurt by status problem or highly accurate move)
* This is also optional,never try using a 5PP move because it's accuracy maybe too low,it runs out very fast and +1PP only if used by PP Up.

Here's my team in LG with their moves:
* (fire,flying) -Fly (flying),Dragon Claw (dragon),Metal Claw (steel),Flamethrower (fire)
* (psychic) -Psychic (psychic),Shadow ball (ghost),Swift (normal),Aura Sphere (fighting)
* (water,ice) -Surf (water),Waterfall (water),Perish Song (normal),Ice Beam(ice)
* (poison,ground) -Megahorn (bug),Dig (ground),Rock Tomb (rock),Rock Smash (fighting)
* (grass,poison) -Solarbeam (grass),Sludge Bomb (poison),Cut (normal), Sleep Powder (grass)
* (electric) -Thunderbolt (electric),Thief (Dark),Strenght (normal),Thunder Wave (electric)

If you want to know if I complete it here's a chart:

Type:-------/Pokemon move user------/moves
normal-----/Mewtwo,Lapras,Raichu----/Swift,Perish Song,Strenght
fire---------/Charizard------------------/Flamethrower
water------/Lapras----------------------/Surf,Waterfall
electric----/Raichu----------------------/Thunderbolt
grass------/Victreebel------------------/Solarbeam,Sleep Powder
ice---------/Lapras----------------------/Ice Beam
fighting---/Mewtwo,Nidoking-----------/Aura Sphere,Rock Smash
poison----/Victreebel-------------------/Sludge Bomb
ground---/Nidoking---------------------/Dig
flying-----/Charizard-------------------/Fly
psychic---/Mewtwo---------------------/Psychic
bug-------/Nidoking--------------------/Megahorn
rock------/Nidoking--------------------/Rock Tomb
ghost-----/Mewtwo--------------------/Shadow Ball
dragon---/Charizard------------------/Dragon Claw
steel------/Charizard-----------------/Metal Claw
dark------/Raichu---------------------/Thief

Replacements:
*You can replace Victreebel by Vileplume if your're using Fire Red.
*You can replace Lapras by Dewgong.

You may post your teams with 17 types as well by different Starter or other versions.You may suggest to replace something or in my tips.

That's true, but on a team having every attack type is not actually necessary. In-game, its easy to sweep out opponents using STAB moves, and in competitive its better to have a well rounded team then to have an attack of every type. To sweep, many sweepers just need to have an Atk/SpA boosting move/item and a way to do normal damage to most opponents. For SE moves, the types you want to have are those that can SE common walls, such as Fire for Skarmory and Bronzong and Fighting for Blissey.

Yep. In ingame, use whatever you want, 100 lvele magikarp is just easy as with lv. 100 Ev trained and breeded team. In competive battling, teams like you have wont have any effect. All you need is that you cover the main threats (for example: Metagross, Tyranitar, Salamence, Blissey and Skarmory, there are many more).

Yes, you maybe right. But I have advantages against opponents who they may be.
And advantages gives 2X damage plus raising them to Lv.100.Even without STAB I can still win,besides I have some moves with STAB like Raichu with Thunderbolt,Lapras with Surf,Waterfall and Ice Beam and Mewtwo with Psychic.

Having all 17 types of moves isn't entirely the best thing. The important thing is that with the types of moves you have, you want to be able to counter the more common types or Pokemon.

For example, Ghost isn't really needed, as Dark has the exact same advantages (Ghost, Psychic), and can also hit on Normal types. Ghost has it over Dark by getting super-effective hits on Medicham, but Medicham is just one Pokemon, and can be shot down with other moves.

Earthquake and Surf hit for decent damage on tons of types, and Grass is the only type able to resist them both.

The team you attempt to build should consist of Pokemon who are proficient and solid in their roles (for example, if you wanted a Steel-type wall, would you call in Mawile? No; you would call in Registeel or Bronzong), and it's also nice to fight with your favorites. Having at least 1 STAB move on sweepers or other attackers is nifty as well, as the base power will hit much higher than other moves with the same base power.

Solarbeam
Sluge Bomb
Leech Life
Flash


Dragon Rage
Hyper Beam
Fire Blast
Fly


Thunderbolt
Cut
Faint Attack
Shadow Ball


Surf
Rock Smash
Dig
Psychic


Waterfall
Strength
Ice Beam
Iron Tail


Rock Tomb
Hydro Pump
Ice Beam
Ancient Power

Type:-------/Pokemon move user------/moves
normal-----/ ----/Cut,Flash,Strength, Hyper Beam
fire---------/ --------------------------------/Fire Blast
water------/ --------------------/Surf,Waterfall
electric----/ -----------------------------------/Thunderbolt
grass------/ --------------------------------/Solarbeam,
ice---------/ -------------------/Ice Beam
fighting---/ -----------------------------------/Rock Smash
poison----/ --------------------------------/Sludge Bomb
ground---/ -----------------------------------/Dig
flying-----/ ---------------------------------/Fly
psychic---/ -----------------------------------/Psychic
bug-------/ --------------------------------/Leech Life
rock------/ ----------------------------------/Rock Tomb, Ancient Power
ghost-----/ -----------------------------------/Shadow Ball
dragon---/ ---------------------------------/Dragon Rage
steel------/ ---------------------------------/Iron Tail
dark------/ -----------------------------------/Faint Attack

Every Hm Possible and Still Have Starter!

I have found that it is impossible to do this without six pokemon.