One) Incorrect conditions

You have the following written in your conditions:

-- (the following is incorrect)
if a >= b < c then

This is actually equivalent to

-- (the following is incorrect)
if a >= (b < c) then

Which is equivalent to

-- (the following is incorrect)
if a >= false then

which makes no sense since a number is not larger than false.

You need to explicitly give the second condition:

if a >= b and a < c then

Two) Dropping part of incorrect condition

HOWEVER, the >= check is unnecessary with the way you are using else! You just need the < check.

Three) Variables instead of repeating ourselves

We can also shorten this by replacing Player.Exp.Value in all of the conditions with a variable; we can shorten Player.leaderstats.PlayerLevel to a variable too. This had typos a few times. This is why you don't organize scripts like this!

Four) Default cases

Finally, your final condition should just be else rather than elseif xp then, and the 'error' cannot occur.

Full script (no loop / formula)

while wait() do
    Player = game.Players.LocalPlayer;
    local xp = Player.Exp.Value;
    local level = Player.leaderstats.PlayerLevel;
    if xp < 300 then
        level.Value = 2
    elseif xp < 600 then
        level.Value = 3
    elseif xp < 1000 then
        level.Value = 4
    elseif xp < 1500 then
        level.Value = 5
    elseif xp < 2000 then
        level.Value = 6
    elseif xp < 2500 then
        level.Value = 7
    elseif xp < 3000 then
        level.Value = 8
    elseif xp < 4000 then
        level.Value = 9
    elseif xp < 5000 then
        level.Value = 10
    elseif xp < 6500 then
        level.Value = 11
    elseif xp < 8000 then
        level.Value = 12
    elseif xp < 9500 then
        level.Value = 13
    elseif xp < 11000 then
        level.Value = 14
    elseif xp < 12500 then
        level.Value = 15
    elseif xp < 14000 then
        level.Value = 16
    elseif xp < 15500 then
        level.Value = 17
    elseif xp < 18000 then
        level.Value = 18
    elseif xp < 21000 then
        level.Value = 19
    elseif xp < 25000 then
        level.Value = 20
    elseif xp < 30000 then
        level.Value = 21
    elseif xp < 35000 then
        level.Value = 22
    elseif xp < 40000 then
        level.Value = 23
    elseif xp < 45000 then
        level.Value = 24
    elseif xp < 50000 then
        level.Value = 25
    elseif xp < 57500 then
        level.Value = 26
    elseif xp < 65000 then
        level.Value = 27
    elseif xp < 72500 then
        level.Value = 28
    elseif xp < 82500 then
        level.Value = 29
    elseif xp < 100000 then
        level.Value = 30
    else
        level.Value = 31
    end
    y = 100 * level.Value
    Player.HP.Value = 200 + y
    Player.Character:WaitForChild("Humanoid").MaxHealth = Player.HP.Value
end

Much shorter version using a table

local xps = {0,3, 6, 10, 15, 20, 25, 30, 40, 50,
    65, 80, 95, 110, 125, 140, 155, 180, 210,
    250, 300, 350, 400, 450, 500, 575, 650, 725,
    825, 1000};
-- Just a list (divided by 100 to be smaller)

while wait() do
    Player = game.Players.LocalPlayer;
    local xp = Player.Exp.Value;
    for level  = 1, #xps do
        if xp >= xps[level] * 100 then
            Player.leaderstats.PlayerLevel.Value = level;
        end
    end
    Player.HP.Value = 200 + 100 * Player.leaderstats.PlayerLevel.Value;
    Player.Character:WaitForChild("Humanoid").MaxHealth = Player.HP.Value
end

Final Concern with Character

I am unsure whether or not this will actually be an issue; in addition to making sure the Humanoid exists like you do in the final line inside the loop, you should probably also be sure that the Character is not nil as well (if Player.Character then { humanoid stuff } end)

-- Try this if you're not going to use tables
game.Players.PlayerAdded:connect(function()
while true do
wait()
if Player.leaderstats.PlayerLevel.Value >= 1 and Player.Exp.Value == 100 then
wait(1)
print(Player.Character.Name.." Has ranked up!")
elseif Player.leaderstats.PlayerLevel.Value <= 1 and Player.Exp.Value ==  >100 then
print(Player.Character.Name.."Doesn't have enough EXP!")
        end
    end
end)