To the OP, you r question is really too vague for us to help you properly. I do not have a camera that uses custom picture styles so bare with me. As far as I understand it you can use DPP to edit the picture style, or to create your own picture style from scratch. These picture styles can then be uploaded to the camera. This is the only form of editing of any file that can be done (as far as I know for any software) that the camera can then see. The camera cannot see any file that has had any sort of post processing editing done to it even if that image has been left on the memory card.
The Canon picture styles only actually affect the image when you are shooting in JPEG's. In that case all the settings from your camera style will be applied to the image when the .JPG is created. This is exactly the same as if you had used one of Canon's own pre installed camera styles.
Now if you are shooting RAW then the picture style settings are not applied to the actual raw data in the file, so it won't change any of the picture data in the RAW file. Now within the RAW file there is also a lot of other information stored as well in the EXIF. Now a lot of the things stored in the files EXIF data are standardised, things like the shutter speed, ISO, lens focal length, white balance etc. As well as all the defined fields the standard also allows camera manufacturers to insert custom information into the EXIF data. The problem is that unless you know specifically what information is stored where and how it is encoded it is just a lot of 1's and 0's. Now Canon use the Manufacturers section of the EXIF data to store all of the information from the picture style that is in use. They actually put all of the data in the file every time, so that you can have your custom settings carry over.
When you download a RAW image to the computer and open it in DPP the program knows how to read the Canon proprietary data from the EXIF data and can then use that information to change the settings used by DPP to match those that would have been used by the camera if it had generated a .JPG in the camera. Now to part of the thing that causes a lot of confusion, as well as the raw image data and the EXIF data the RAW file also contains a preview image, this is effectively an in camera generated .JPG image that is in-bedded within the .CR2 RAW file. Now the camera uses the Canon camera styles when it generates this .JPG file so when you see the image preview in any software for a RAW file, even in the operating system file browser if it is supported, what you see is the .JPG part of the RAW file that has been extracted.
So if you use any other RAW conversion software than Canon's DPP then unfortunately those applications cannot read the data from the proprietary part of the EXIF data, so those settings cannot be applied to the image. Also all RAW converters work differently, and will produce different results from the same RAW file. Even different versions of software may have different controls that change how the image will be converted, for example Adobe Lightroom recently went from version 3.x to 4.x and there were many changes to the way the conversions are done between the two versions of LR. What this means is that all other RAW converters have to start from default settings for every image. Now most other (than DPP) RAW converters allow you to apply different default settings to images as you import them, or open the file, and it is usually quite easy to change the default settings as well. Often the default settings will have been set up by the oftware manufacturer so that when applied to a file they closely mimic the effects of changing the Picture style in DPP, and often they are given similar sounding names, such as Faithful, Landscape etc.
Finally for RAW conversion software, all the changes made to the file are non destructive, in other words they can be undone. Also as all the different programs do things differently there are two issues. The first is how to store the details of what changes have been made. For DPP as it has access to Canon's proprietary EXIF data encoding system, DPP writes the list of control changes (because that is how all of the converters save the information on changes) into the EXIF of the actual file. Most other programs either write a list of the changes made to the image that is stored on the hard drive in the folder with the .CR2 file. Adobe use files that have the same name but an .XMP extension. All of the different converters use a different file format though. Delete the .XMP file and you delete all the changes you made in the Adobe RAW converter. The other option is to store all the changes you make to all files in a Database. Actually Adobe also use this system in LR. LR also uses .XMP files if you should want to have compatibly with ACR the RAW converter provided with Photoshop.
So what dose this all mean to us.
1. If shooting in camera JPEG, all the picture style settings are used when the camera generates the .JPG file. These settings are permanently "Baked" in to the image.
2. If shooting RAW then the picture style settings are used to generate the preview image that is stored within the .CR2. All of the settings are also stored in the .CR2 files EXIF data.
3. For RAW files only Canon's own DPP software can read and make use of the picture style information in the EXIF part of the .CR2 file.
4. Other RAW converters always start from some base default set of settings, although they can be changed and often are, with descriptive names that allow them to at least start with a set of settings that approximate those you would have go from Canon's default picture style settings. These other programs though cannot read any of this data so cannot know what picture style was set in camera.
5. Because all RAW converters do different things and have different controls it is not possible for different RAW processors to interchange settings (apart from some Adobe products that can be setup to be consistent between applications). So it is not Possible to start your conversion in DPP because it supports picture styles, and then open the same file, with the DPP settings maintained, in say LR because the noise control is better (just one possible example).
6. There is no RAW converter that is also good at pixel level retouching using advanced techniques such as layers. This means that you have to convert the image to a different format if you need to then do pixel level editing, and you then loose the flexibility of the RAW file. AT this point though you should have done all of the major global changes to the image, things affecting colour balance, exposure, noise reduction etc should be done in the RAW converter where possible before moving on to the pixel level editing. I would always suggest using TIFF or if using Photoshop PSD for the file format for images that you are going to edit in this way as they allow you to save them with layers intact. JPEG is not a good format for this, although it is most likely to be the format you end up in.
Please also note that for RAW files the colour balance used and the orientation (landscape / portrait) are stored in the defined EXIF and are therefore available to all applications, so colour tone and auto-rotation of images if used is preserved.