Well, Google+ doesn't have a "wall," it has "Streams." The proper term might help you find better search results. Either way, unless you're a Google partner, the news isn't good:
The API is currently limited to read-only access. From the API website:
Note: The Google+ API currently provides read-only access to public
data. All API calls require either an OAuth 2.0 token or an API key.
Because it's read-only, you will not be able to update or post any information anywhere through the API -- you can only use it to pull basic information like profile and activity details.
Given that access to the API may change over time, I'll try to keep this answer up to date with information about news or changes related to write access.
News & Updates
2015-04-28: Google+ Domains API was announced way back in August 2013, but somehow I missed its relevance to Google+.
The Google+ Domains API allows Google Apps customers and ISVs to take advantage of enhanced Google+ APIs to build tools and services that can be used in a variety of ways.
No, it does not provide full write access to a user's Google+ profile, but it does give you minor advantages over the Google+ API v1, at least within a domain. This one's mainly for mobile app developers.
2015-01-21: I have revisited many of the sources linked in this answer and searched for news regarding API changes, but Google has been quiet.
2014-03-12: Various discussion threads on Google+ about write access (or lack thereof):
2013-12-03: The issue thread from UPDATE 1 has finally been responded to by a Google+ project member. Additional discussion regarding write-access to Streams is taking place intermittently on the Developing with Google+ community page.
2013-07-05: A developer named Eric Leroy has built an "unofficial" JavaScript library that provides read/write extension to the Google+ API.
2013-05-14: A "social media management company" can gain additional API access by attempting to become a Google+ Pages API Partner.
Here's an excerpt from the Partner Application Form:
The Google+ pages API allows social media management companies to add Google+ page management features into their tool. Access to this API is available through a whitelist, and access is granted to partners on a company by company basis dependent on fit with this API.
Other articles explaining the lack of a write API:
2013-01-04: Google just announced Google+ History. You can use it to write "moments" (which are private by default) but can then be made public by sharing them directly to your stream and/or your profile. One of the moment types is CommentActivity.
2012-10-08: There's now a duplicate bug post with only a few comments, but you can check there for future updates as well.
2012-06-25: I came across the issue tracker post for Google+ Write Access. The enhancement request status is "New" and priority is "Medium" as of June 25th, 2012. There are some links of interest in the comments.
