Last fall, in one of the stranger and more expensive efforts to boost company morale, Yahoo CEO Marissa Mayer decided that all her executive staff needed to play dress-up.

In an elaborate photo shoot that took place at an offsite at the Cavallo Point Lodge in Marin County, north of San Francisco, she cast all the top staffers as characters from “The Wizard of Oz” and made them pose for a poster in full costume, since it was to be the theme of the upcoming employee holiday party.

Emerging product head Adam Cahan was the Scarecrow; former development chief Jackie Reses was the Wicked Witch; communications head Jeff Bonforte was the Tin Man; CIO Laurie Mann was the Cowardly Lion; media and marketing boss Kathy Savitt was Glinda; top lawyer Ron Bell was a flying monkey; and CFO Ken Goldman was the Wizard.

And Mayer? Dorothy, of course, with a stuffed animal as Toto.

The effort cost $70,000, according to many sources, and caused some level of consternation among staffers. “It was very embarrassing, but Marissa thought that it was the way to make employees in Silicon Valley happy,” said one person there. “We really could not argue.”

It was classic Mayer, who is well known in the tech community for her over-the-top personal holiday parties, which have even included a made-from-scratch ice rink and Mayer riding a mini-Zamboni on it.

All fun and clearly creative, but many felt the shoot was indicative of a leader who has pulled Yahoo down a lot of time-sucking detours in her laborious efforts to turn around the long-troubled company.

Silly photo shoots aside — I think it was kind of corny in a good way — that has manifested itself more critically in a herky-jerky series of strategic moves that have swung Yahoo to and fro. It’s included an intense focus on media by making big bets on digital magazines to pricey video deals to a questionable race to compete with giants like Google in search.

It has also been characterized by a lot of seemingly disjointed acquisitions that appear aimed more at bringing in talent to the company than any cogent direction. Mayer has no clear strategy head or chief product officer, save herself, which many think has been an issue.

Even purchases that did not happen are hard to grok, such as one of invitation site Paperless Post, which Mayer wanted to pay $48 million for last year to bring more “creativity” to Yahoo. The deal got down to the term sheets, but was abandoned after some internal dissent.

Another Mayer obsession for a while that went nowhere: Getting television’s hottest hit-maker, Shonda Rhimes, to make an original show for Yahoo. Yahoo did do a series of such deals, most of which were written down in the recent quarter.

Wall Street has largely ignored the many shifts, due to the cover that Mayer and Yahoo have been provided by its longtime investment in China’s Alibaba Group. The stake has kept its stock aloft since Mayer arrived more than three years ago and allowed her a lot of breathing room, too.

But with the spinoff of that asset coming soon, many inside and outside the company are wondering if Mayer knows the answer to what the core of Yahoo will be going forward. To help her, Yahoo hired McKinsey & Co. to sort out what should be cut, what should be sold and what should be focused on.

The effort has been known internally as Project Family Business, under the guiding premise that products should not be built in different countries, but in a centralized way in Silicon Valley. It started in earnest last year with cuts across the globe and now is being intently aimed at a more serious change in the core company business as the Alibaba spinoff nears completion.

Which direction Mayer will take is now the pressing question inside Yahoo, which seems to have boiled down to a choice between focusing more on media or search, Yahoo’s two main money-makers.

Mayer began her tenure with a series of splashy media moves, such as the $1 billion purchase of Tumblr, the hiring of high-profile journalists like Katie Couric and the backing of big video efforts.

But her efforts now, said sources, seem to be mostly aimed at Project Index, an effort to create an “indispensable digital guide” for consumers. Built around Yahoo’s mail, it boils down to a massive attempt to rethink mobile search. Once led by Bonforte, Mayer has turned the job over to search head Enrique Torres, who is — like Mayer — a former Googler.

Sources said Mayer is pinning her hopes on Project Index, which was shown at another exec offsite last month (where no dress-up was required).

One person who saw it said it was an interesting effort, but was not the game-changer Yahoo needs in what has been a quickly shifting digital landscape. But sources said the launch was still a ways off, even as far as late next year. That raises the question of what Yahoo will be once it is free of Alibaba (and, eventually, another lucrative stake in Yahoo Japan). So far, said insiders, that answer is still in flux.

Representatives of Yahoo declined to comment.

One thing is clear: Yahoo’s not in Kansas anymore.