I turn the camera off, it turns off, 15-20 seconds later it will turn on by it's self

Sounds like you have the "self-timer" turned on. That should be on the menu to turn it off.

Manual:
http://www.kodak.com/global/plugins/acrobat/en/service/manuals/urg01041/C182_xUG_GLB_en.pdf

Page 11

Using the self-timer
Use the self-timer when you want to be included in a picture, or to ensure a steady
Shutter button press. Place the camera on a tripod or flat surface.
1 In any picture-taking mode, press the Info button to turn on the shortcut icons.
2 Press to highlight the self-timer icon. Press to choose a setting:
10 seconds- A picture is taken after a 10-second delay (so you have time
to get into the scene).
2 seconds- A picture is taken after a 2-second delay (for a steady, shutter
release on a tripod).
2 shot- The first picture is taken after a 10-second delay. A second picture
is taken 8 seconds later.
3 Compose the scene. Press the Shutter button halfway, then completely down.
The camera takes the picture/pictures after the delay.
Use the same procedure to take a 2- or 10-second self-timer video, but press the
Shutter button completely down.

In any still mode, press the Menu button. Press up/down to highlight Self-Timer, then press OK. Press up/down to choose between 10-second, 2-second, and 2-shot (one picture after 10 seconds, a second shot 8 seconds later). Press OK, then the Menu button. Start the self-timer by pressing the shutter release button.

Hi, Follow these steps:
1. In any Still mode, tap Settings to open the Settings panel.
2. Tap Self-Timer/Burst repeatedly, until the desired Self-timer icon appears at the bottom of the LCD: 10 seconds—A picture is taken after a 10-second delay (so you have time to get into the scene). 2 seconds—A picture is taken after a 2-second delay (for a steady, auto-shutter release on a tripod). 2 shot—The first picture is taken after a 10-second delay. A second picture is taken 8 seconds later.
3. Compose the scene. Press the Shutter button halfway, then completely down. The camera takes the picture/pictures

Make sure you're in a recording mode other than VOICE.

Press the Self-Timer button (right button) until the display shows the desired mode. Your choices are 10-second mode (the camera takes a picture ten seconds after you press the shutter button), 2-second mode (the camera takes a picture two seconds after you press the shutter button), and Double-self-timer (the camera takes a picture ten seconds after you press the shutter button, then takes another two seconds later).

You can cancel the self-timer mode by pressing the Self-Timer button again.

The 10-second mode allows you to run back for a group picture. The 2-second mode is useful when you want to take a picture without fear of camera shake; simply place the camera on a steady support such as a tripod. The Double mode increases the chances of getting a picture with everybody's eyes open.

This is probably THE single most common failure among digital cameras. There's a halfway chance of fixing it yourself, described here: http://camerarepair.blogspot.com/2007/12/fixing-lens-error-on-digital-camera.html

1 In any Still mode, tap Settings to open the Settings
panel.
2 Tap Self-Timer/Burst repeatedly, until the desired
Self-timer icon appears at the bottom of the LCD:
10 seconds—A picture is taken after a 10-second
delay (so you have time to get into the scene).
2 seconds—A picture is taken after a 2-second
delay (for a steady, auto-shutter release on a
tripod).
2 shot—The first picture is taken after a 10-second
delay. A second picture is taken 8 seconds later.
3 Compose the scene. Press the Shutter button halfway, then completely down.
The camera takes the picture/pictures after the delay.

In any Still mode, press down-arrow repeatedly until the self-timer icon appears for the desired setting. Your choices are 10-second delay, 2-second-delay, and 2-shot, where one picture is taken after ten seconds and a second picture eight seconds later.

In any Still mode, press down-arrow repeatedly until the self-timer icon appears for the desired setting. Your choices are 10-second delay, 2-second-delay, and 2-shot, where one picture is taken after ten seconds and a second picture eight seconds later.

Hi there,
by the way in setting the timer for your camera here is what you are going to do...

-turn the camera on
-set the camera in recording
-press the Right Button beside the menu button (the incomplete circle)
-and then you will see that there will an icon showing in the left side part of the screen of the camera.

Selecting the self-timer
1. Rotate the MODE DIAL to select a RECORDING mode with the exception of VOICE RECORDING mode.
2. Press the SELF-TIMER button until the desired mode indicator displays on the LCD monitor.
A 10 second, 2 second or double self-timer icon appears on the LCD monitor. In Movie Clip mode, only the 10-second self-timer will work.
•2SEC self-timer (icon of incomplete circle with 2S)
: Pressing the shutter button will allow an interval of 2 seconds before the image is
taken.
•10SEC self-timer (incomplete circle)
: Pressing the shutter button will allow an interval of 10 seconds before the image is taken.
•Double self-timer (double incomplete circle)
: A picture will be taken after about 10 seconds and 2 seconds later a second picture will be taken. When using the flash, the 2-second self-timer may be delayed for longer than 2 seconds depending on the flash charge time.
3. When you press the SHUTTER button, the picture will be taken after the
specified time has elapsed.